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

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Answer 1 · 2016-05-01T06:56:45

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

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.

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

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

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