How do you differentiate y=3y44u+5;u=x32x5 using the chain rule?

1 Answer
Oct 9, 2017

dydx=12x2+8112y3

Explanation:

When we put the value of u in y we get

y=3y44(x32x5)+5

y=3y44x3+8x+25

When we differentiate both sides with respect to x we apply chain rule.

ddxy=ddx(3y44x3+8x+25)

dydx=12y3ddxy12x2ddxx+8

dydx=12y3dydx12x2+8

dydx12y3dydx=12x2+8

dydx(112y3)=12x2+8

Therefore

dydx=12x2+8112y3