### Home > CALC > Chapter 5 > Lesson 5.3.2 > Problem5-122

5-122.

Find the derivative of each function.

1. $f ( x ) = x \sqrt { 5 - x ^ { 2 } }$

This derivative involves both the Product Rule and the Chain Rule.

$f'(x)=\frac{5-2x^{2}}{\sqrt{5-x^{2}}}$ Show the steps!

1. $g(x) = 2\operatorname{cot}(5x) − 2\operatorname{ cos}^3 x$

Be very careful to keep track of positive and negative coefficients.