Question

What is the derivative of `m(x)= (5^x)(x^7)`?

Answer 1

`m'(x)=5^x x^6(7+x ln 5)`

Explanation:

Using the rule for the product,

`m'(x)=(5^x)(x^7)'+(x^7)(5^x)'`.

`=7 x^6 5^x + x^7(e^(x ln 5))'`

`=7 x^6 5^x + x^7(e^(x ln 5)) ln 5`, using function of function rule.

`=7 x^6 5^x + x^7(5^x) ln 5`.

`=5^x x^6(7+x ln 5)`