Calc2.17

From Exampleproblems

Find the derivative of $f(x)\,$ with respect to $x\,$ : $f(x)=(x^3+7x)^3\,$

This is the Generalized Power Rule, a special case of the Chain Rule. We have a function to a power. As with the power rule, bring down the power and subtract one from the exponent. In addition, the chain rule tells us to multiply by the derivative of the inside function.

$f'(x)=3(x^3+7x)^2(3x^2+7)\,$