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 teh second term?
never mind, the second term is derived using the product rule
Chain Rule with single variable:
Chain Rule with multiple variables:
The y and the (x-4) 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.
But (2x-4) and y aren't the same as x, and neither are the derivatives. So the chain rule will produce something appreciable. The derivative of 2x-4 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.
Answer this Question
calculus help - implicit differentation 1.y^3=4(x^2+y^2) 2.y^2-3x+2y=0 help ...
Math - Calculus Question. - hey can someone explain to me the relationship ...
Calculus - How do I use the chain rule to find the derivative of square root(1-x...
Calculus - Derivative Differentiate f(x)=(5x-4)^2 There are two ways to do this...
Calculus - Use implicit differentiation to find dy/dx. e^4x = sin(x+2y). This is...
MoRe HeLp PlEaSe!! (calc) - Also can I get some help with this LONG, TIRESOME ...
Math, Calculus - Find the derivative of the function. y= xcosx - sinx What's the...
calculus - I have been asked to solve this two different ways. The first way is...
Calculus - Find dy/dx by implicit differentation. ysin(x^2)=-xsin(y^2)
Calculus - Can anyone explain how to use the chain rule and power rule together ...