CPM Homework Help : CALC3RD Problem 6-38

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6-38.

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

$y=2^{\log_2(x)}$
Hint (a):
$2^{\log_2(x)}=x$

$y = \tan(10^x)$
Hint (b):
Use the Chain Rule.
Answer (b):
$y' = (\sec^210^x)(\ln 10) · 10^x$

$y = \cos(t)\tan(t)$
Hint (c):
$\text{tan}x=\frac{\text{sin}x}{\text{cos}x}$

$y = \tan(e^x)$
Hint (d):
Use the Chain Rule. $\frac{d}{dx}e^{x}=e^{x}$

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

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