Question

How do you differentiate `y=x^3(2x-5)^4`?

Answer 1

Using the product rule `(1 xx d2 + 2 xx d1)`, you would set 1 as `x^3` and 2 as `(2x-5)^4`.

The derivative of 1 would be `3x^2` and the derivative of 2 is `4(2x-5)^3 *2`, or `8(2x-5)^3` using the chain rule.

Now plug in the values into the product rule, so that `(x^3 xx 8(2x-5)^3) + ((2x-5)^4) xx 3x^2)`.

This expanded is `112 x^6 - 960 x^5 + 3000 x^4 - 4000 x^3 + 1875 x^2`.