Chain rule

Welcome to the "Chain rule" category on Questions LLC! This is the perfect place for all your queries and discussions surrounding the fascinating concept of the chain rule in mathematics. Whether you're a student looking for a better understanding of this rule or a curious mind wanting to explore its applications, you've come to the right place. Our community of experts, enthusiasts, and learners are here to provide insightful answers and engage in thought-provoking discussions. So, dive in, explore the various questions, and unravel the intricacies of the chain rule with us!

Questions (45)

f is a differentiable function on the interval [0, 1] and g(x) = f(2x). The table below gives values of f ′(x). What is the
1. 5 answers
2. asked by Anon
3. 12,360 views
Use chain rule to find dz/dt.z=tan^-1 (y/x) , x=e^t, y=7-e^(-t)
1. 1 answer
2. asked by Paul
3. 59 views
Use the Chain Rule, in Leibniz notation, to find dy/dx at the indicated value of x. y=u(u^2+3)^3, u=(x+3)^2, x=-2
1. 2 answers
2. asked by m
3. 87 views
1.)Find dy/dx when y= Ln (sinh 2x)my answer >> 2coth 2x. 2.)Find dy/dx when sinh 3y=cos 2x A.-2 sin 2x B.-2 sin 2x / sinh 3y
1. 4 answers
2. asked by anon
3. 2,899 views
Use the Chain Rule to find ∂z/∂s and ∂z/∂t.z = tan(u/v), u = 7s + 4t, v = 4s − 7t
1. 4 answers
2. asked by Becky
3. 2,759 views
Use the Chain Rule to find dw/dt.w = ln (x^2 + y^2 + z^2)^.5 , x = 9 sin t, y = 6 cos t, z = 7 tan t
1. 4 answers
2. asked by Becky
3. 5,396 views
Let H(x)=F(G(x)) and J(x)=F(x)/G(x).Suppose F(7)=4, F′(7)=−8 G(7)=3, G′(7)=−5 G(2)=7, G′(2)=−2 then H′(2)=
1. 5 answers
2. asked by Anonymous
3. 794 views
f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(2x)]. The table below gives selected values for f(x),
1. 6 answers
2. asked by Henry
3. 7,176 views
Complete the table.y = f(g(x)) u = g(x) y = f(u) y = (2x − 4)^7 u = y= This problem involves the chain rule of derivatives.
1. 3 answers
2. asked by Lorine
3. 1,265 views
find d/dx (integral from 2 to x^4) tan(x^2) dxtan(x^4)^2*4x^3 MY ANSWER
1. 4 answers
2. asked by Ke$ha
3. 1,035 views
88. (a) Write | x | − sx 2 and use the Chain Rule to show thatd dx | x | − x| x | (b) If fsxd − | sin x |, fnd f9sxd and
1. 1 answer
2. asked by 余才垚
3. 301 views
Complete the table.y = f(g(x)) u = g(x) y = f(u) y = (x + 18)^(-1/2) u = ? y=? Use the chain rule.
1. 2 answers
2. asked by Lorine
3. 801 views
Find the derivative of cos(sqrt(e^(x^3)cos(x))I got -sin(sqrt(e^(x^3)cos(x))*((sqrt(e^(x^3)cos(x)) Do I just leave the
1. 4 answers
2. asked by Z32
3. 515 views
We now haved dx [x5 + y8] = 5x4 + 8y7y' = d dx [9] = 0. Rearranging this, we get 8y7y' = ??????????
1. 4 answers
2. asked by Anonymous
3. 2,767 views
Use the chain rule, in Leibniz Notation, to find dy/dx at the indicated value of x.y = u^3 - 2(u - 3)^4, u = x + x^1/3, x = 1
1. 1 answer
2. asked by help me pls
3. 254 views
what is derivative of 4(x-3)^2 using CHAIN RULE please
1. 1 answer
2. asked by mofazid
3. 412 views
f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(5x)]. The table below gives selected values for f(x),
1. 2 answers
2. asked by Rich boi
3. 1,198 views
Show that if f(x) is continuous and u(x) and v(x) are differentiable functions, then:d/dx ∫_v(x)^u(x)
1. 1 answer
2. asked by Katy
3. 377 views
Given u(x, y) = x^2 + 2y where x (r, t) = r sin(t) and y(r,t) = sin^2(t), determine the value of ∂u / ∂r and ∂u / ∂t
1. 3 answers
2. asked by payuto
3. 463 views
Compute d/dx(f(g(x)))-where f(x)= square root of x -and g(x)=x^2+7
1. 1 answer
2. asked by Dominick
3. 304 views
The mass, M, of a child can be approximated based on the height, H, of the child. The height of the child can be projected based
1. 2 answers
2. asked by Anonymous
3. 518 views
Use the chain rule and simplify your answer: y= 1/u prime u= 3x^2 + 5
1. 1 answer
2. asked by Ebian
3. 290 views
The cost of producing x units of a product is C = 60x + 1350. For one week management determined the number of units produced at
1. 2 answers
2. asked by Lorine
3. 990 views
Differentiate with respect to (t).y = d cos(t) + (t^2)sin(t)
1. 2 answers
2. asked by Melish
3. 614 views
Find f '(a).f(x)= sqrt(1 − 6x)
1. 2 answers
2. asked by Leigh
3. 490 views
Compute d/dx[f(g(x))]-where f(x)=x^4-x^2 -and g(x)=x^2-7 (Note: I tried 5 times but I still got this wrong. Plz help)
1. 1 answer
2. asked by Dominick
3. 341 views
using the chain rule find the min and max points and their values of the composite function defined by z=x^2+y^2, x=sin(2t),
1. 5 answers
2. asked by Lucy
3. 457 views
Find the first derivative for the following functions1) f(x) = sin(cos^2x) cos(sin^3x) 2) f(x) = ( tan 2x - tan x ) / ( 1 + tan
1. 1 answer
2. asked by Yousef
3. 485 views
Given f, a derivable function andy = f (x)^3 + 40√(f(x)+12) . Knowing that f(4) = -4 and that dy/dx|x=4 = 14 , calculate
1. 1 answer
2. asked by Ralph
3. 284 views
Hi, I'm trying to figure this out, but the answer I keep coming up with is incorrect. Can anyone help me out? Thanks.Problem:
1. 1 answer
2. asked by Dale
3. 367 views
Hi could someone please explain to me how i would use the chain ruledy/dx = dy/du(du/dx) to solve for y= sin(x+y) - im looking
1. 3 answers
2. asked by sarah
3. 384 views
How do you find f'(x), f''(x) of f(x) =ln (1-x)IF f(x) = ln (1-x) Then use the chain rule with u(x) = 1-x f(u) = ln u df/dx =
1. 1 answer
2. asked by Jill
3. 465 views
I've been having some difficulities with this but I think I figured it out. Could you double check me and make sure I'm doing
1. 1 answer
2. asked by becky
3. 536 views
Let f and g be the functions in the table below.x f(x) g(x) f '(x) g'(x) 1 3 2 4 6 2 1 3 5 7 3 2 1 7 9 (a) If F(x) = f(f(x)),
1. 3 answers
2. asked by Gabe
3. 1,693 views
Solve using chain ruley=(3x^3+1)(-4x^2-3)^4 So far, I have: y'=(3x^3+1)*4(-4x^2-3)^3*(-8x)+(-4x^2-3)^4*(9x^2)
1. 2 answers
2. asked by Mike
3. 1,138 views
I finished this problem but I wanted some feedback because I don't know if it's entirely correct.Suppose that functions f and g
1. 3 answers
2. asked by Lauren
3. 835 views
Suppose f and g are functions that are differentiable at x = 1 and that f(1) = 2, f '(1) = -1, g(1) = -2, and g '(1) = 3. Find
1. 1 answer
2. asked by Mike
3. 582 views
Jena. Stop it, or you will be banned.Using the chain rule, how do i solve this problem? g(x)=(sin3x)^3 g'(x)=?? 3sin(3x)^2 • 3
1. 1 answer
2. asked by bobpursley
3. 576 views
Could someone check my reasoning? thanxFind the derivative of the function. sin(sin[sinx]) I need to use the chain rule to
1. 2 answers
2. asked by XCS
3. 613 views
Assume that x>0 and y>0. If y=5sqrt{x+9} and dx/dt = 2, find dy/dt when x=7.
1. 2 answers
2. asked by Raj
3. 527 views
Find F '(x) for F(x) = integral[x^3 to 1](cos(t^4)dt)a. cos(x^7) b. -cos(x^12) c. -3x^2cos(x^12) d. cos(1) - cos(x^12)
1. 2 answers
2. asked by Jimmy
3. 533 views
I heard that when we are proving Leibniz's formula for differentiating an integral, we use chain rule i.e.dw/dx=(�Ýw/�Ýu)(du
1. 2 answers
2. asked by masaya
3. 534 views
Find f'(x) if f(x)=sin^3(4x)A. 4cos^3(4x) B. 3sin^2(4x)cos(4x) C. cos^3(4x) D. 12sin^2(4x)cos(4x) E. None of these I got D using
1. 2 answers
2. asked by Anonymous
3. 504 views
What is the derivative of f^3(g(x)) where both are continuous functions?I used chain rule and got 3f^2(g(x))f'(g(x))g'(x) but it
1. 1 answer
2. asked by Andre
3. 436 views
why do we use chain rule for deriving ln(x^2+5x)
1. 3 answers
2. asked anonymously
3. 17 views