### Home > CALC > Chapter 6 > Lesson 6.1.3 > Problem6-38

6-38.

Differentiate the following functions with respect to the given independent variable.

1. $y = 2^{\operatorname{log}_2(x)}$

2log2x = x

1. $y =\operatorname{tan}(10^x)$

Use the Chain Rule.

y' = (sec210x)(ln 10) · 10x

1. $y =\operatorname{cos}(t)\operatorname{tan}(t)$

$\text{tan}x=\frac{\text{sin}x}{\text{cos}x}$

1. $y =\operatorname{tan}(e^x)$

Use the Chain Rule, $\frac{d}{dx}e^{x}=e^{x}$.

1. $y = 2^{\operatorname{cos}(w^3)}$

$y^{\prime}=(\operatorname{In}2)\cdot2^{\operatorname{cos}(w3)}\cdot\operatorname{sin}(w^3)\cdot3w^2$