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6-38.

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

$y = 2^{\operatorname{log}_2(x)}$
Hint (a):
2^log₂x = x

$y =\operatorname{tan}(10^x)$
Hint (b):
Use the Chain Rule.
Answer (b):
y' = (sec²10^x)(ln 10) · 10^x

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

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

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

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