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

5-122.

Write the derivative of each function.

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

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

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

2. $g\left(x\right)=2\cot\left(5x\right)-2\cos^3\left(x\right)$

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