Question

How do you use the chain rule to differentiate `y=x^3(2x-5)^4`?

Answer 1

`dy/dx = x^2(2x-5)^3(14x-15)`

Explanation:

`y =x^3(2x-5)^4`

`dy/dx= x^3 * d/dx(2x-5)^4 + (2x-5)^4 * d/dx(x^3)` (Product rule)

`= x^3 * 4(2x-5)^3 * 2 + (2x-5)^4 * 3x^2` (Power rule and Chain rule)

`= x^2(2x-5)^3(8x+3(2x-5))`

`=x^2(2x-5)^3(14x-15)`