calculus high school
posted by k .
7y^4+x^3y+x=4
using implicit differentation, how do i solve this problem. it is a textbook example but the partwhere i "use the chain rule on the first term" doesn't make sense to me because they get
d/dx 7y^4+(x^3dy/dx +y d/dx x^3)+d/dx x

I get
28y^3(dy/dx) + x^3(dy/dx) + y(3x^2) + 1 = 0
dy/dx(28y^3 + x^3) =  1  3(x^2)(y)
dy/dx = ( 1  3(x^2)(y))/(28y^3 + x^3)
I used he chain rule on the first term, the product rule on the second term, the others were routine 
thanks. you got the answer right. but i don't understand how the chain rule is used iin this problem.

in 7y^4, according to "chain rule"
exponent times front coefficient > 4(7) = 28
keep the base, reduce the exponent by 1 y^4 becomes y^3
times the derivative of the base, the base is y, so derivative of y is called dy/dx
result > 28y^3(dy/dx) 
isn't that the power rule?
anyway, ow do you derive the second term? 
never mind, the second term is derived using the product rule

Chain Rule with single variable:
d/dx [3(2x4)^2]
=6(x4)(2)=12x48
Chain Rule with multiple variables:
d/dx [3y^2]
=6y(dy/dx)
The y and the (x4) terms serve a similar function. You technically use the chain rule all the time. The derivative of a variable, like x, is simply 1. So taking the derivative of 3x^2 is really easy.
d/dx [3x^2]
=6x(1)
But (2x4) and y aren't the same as x, and neither are the derivatives. So the chain rule will produce something appreciable. The derivative of 2x4 is 2, so it affects the expression (whereas the derivative of x is simply one, and multiplying by one changes nothing). Y is also not equal to x. Because we are differentiating with respect to x, d/dx of y cant be 1. And we don't know anything else about y, so all we can do is say that dy/dx equals... well dy/dx.
Respond to this Question
Similar Questions

calculus help
implicit differentation 1.y^3=4(x^2+y^2) 2.y^23x+2y=0 help please You consider y to be a function of x, but you don't explicitely solve for it. Then you formally differentiate w.r.t. x using the chain rule: y^3(x) = 4(x^2+y^2(x)) … 
Math  Calculus Question.
hey can someone explain to me the relationship between the chain rule and implicit differentiation? 
MoRe HeLp PlEaSe!! (calc)
Also can I get some help with this LONG, TIRESOME PROBLEM? 
Calculus
Derivative Differentiate f(x)=(5x4)^2 There are two ways to do this: (1) let u = 5x4, and use the "chain rule", df/dx = df/du * du/dx OR (2) expand the polynomial to f(x) = 25 x^2 40x + 16 and differentialte it termbyterm. You … 
Math, Calculus
Find the derivative of the function. y= xcosx  sinx What's the derivative? 
Calculus
How do I use the chain rule to find the derivative of square root(1x^2) also, are there any general hints or tips for determining when the chain rule and product or quotient rule should be used? 
calculus
I have been asked to solve this two different ways. The first way is to use the chain rule and then simplify (which I have already done properly), and the second way is to simplify and then differentiate (not necessarily with the chain … 
Calculus
Find dy/dx by implicit differentation. ysin(x^2)=xsin(y^2) 
Calculus
Use implicit differentiation to find dy/dx. e^4x = sin(x+2y). This is a practice problem. It says the correct answer is 4e^x/(2sin(x+2y)) but I keep getting 4e^(4x)/(2cos(x+2y)). I thought the derivative of e^(4x) would be 4e^(4x), … 
Math (Calculus)
Hello, Could somebody please help me with the following question?