Question

What is the derivative of `(2x-3)^5`?

Answer 1

`10(2x-3)^4`

Explanation:

Apply the chain rule, which tells us that `d/dx(f(g(x))=f'(g(x))*g'(x).`

For the function `(2x-3)^5,` we see it is a polynomial composed with an exponential function. So, the power rule is used to differentiate the polynomial raised to the `5th` power, and the fact that `d/dxax=a` to differentiate the polynomial `2x-3`

`d/dx(2x-3)^5=5(2x-3)^(5-1)*d/dx(2x-3)`

`=(2)(5)(2x-3)^4=10(2x-3)^4`