How do you differentiate y=(x3+2)2(x5+4)4?

1 Answer
Mar 13, 2018

To differentiate the expression, you could you explicit differentiation or implicit differentiation. I'm going to use implicit differentiation.

Explanation:

Using the chain rule in conjunction with the product rule, we get:

dydx[(x3+2)2(x5+4)4]

=ddx[(x3+2)2](x5+4)4+(x3+2)2ddx[(x5+4)4]

=2(x3+2)ddx[x3+2](x5+4)4+4(x5+4)3ddx[x5+4](x3+2)2

=2(ddx[x3]+ddx[2])(x3+2)(x5+4)4+4(ddx[x5]+ddx[4])(x3+2)2(x5+4)3

=2(3x2+0)(x3+2)(x5+4)4+4(5x4+0)(x3+2)2(x5+4)3

=6x2(x3+2)(x5+4)4+20x4(x3+2)2(x5+4)3

Which, when simplified, is equal to:
=2x2(x3+2)(x5+4)3(13x5+20x2+12)