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

6-38.

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

1. $y=2^{\log_2(x)}$

$2^{\log_2(x)}=x$

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

Use the Chain Rule.

$y' = (\sec^210^x)(\ln 10) · 10^x$

1. $y = \cos(t)\tan(t)$

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

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

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

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

$y^\prime = (\ln 2) · 2^{\cos(w^3)} · -\sin(w^3) · 3w^2$