Differentiate each function. Please show all work/steps.

Question

Differentiate each function. Express your answer in a simplified factored form

1. a) f(x) = (x + 4)³(x - 3)⁶

b) f(x) = sin²(x³- 2x + 4)

Answer 1

In the first one you need to use both the product rule and the chain rule.

In the second one: use the power rule and the chain rule as follows

2 sin (x³-2x+4)(3x²-2)

There is no cos in the 2nd answer...the answer I wrote is complete.

In the first one you got messed up:

3(x+4)²(x-6)⁶+6(x-3)⁵(x+4)³ which you can simply a bit by taking out common factors....but I will leave that to you.