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Compute the derivative of $v(w) = (\ln(w))^2$ .

$v'(w) = 2 (\ln(w)) \frac{1}{w}$ .

Find the derivative of $f(x) = \cos(x^2 + 3x)$ .

$f'(x) = -\sin(x^2 + 3x)(2x + 3)$ .

Differentiate $y = \arcsin(e^x)$ .

$y' = \frac{e^x}{\sqrt{1 - (e^x)^2}}$ .

Find the derivative of $p(t) = \ln(7t + 5)$ .

$p'(t) = \frac{1}{7t + 5}(7)$ .

Differentiate $g(x) = \sqrt{2x + 1}$ .

$g'(x) = \frac{1}{2\sqrt{2x + 1}}(2)$ .

Differentiate $s(t) = (1 - t^2)^{1/3}$ .

$s'(t) = \frac{1}{3}(1 - t^2)^{-2/3}(-2t)$ .

Differentiate $f(x) = \log_3(x^2 + 4x)$ .

$f'(x) = \frac{1}{(x^2 + 4x)\ln 3}(2x + 4)$ .

Compute the derivative of $f(x) = \tan(x^4)$ .

$f'(x) = \sec^2(x^4)(4x^3)$ .

Compute the derivative of $h(z) = e^{z^3 - z}$ .

$h'(z) = e^{z^3 - z}(3z^2 - 1)$ .

Find $\frac{d}{dx}\left[ \frac{1}{\sqrt{x + 1}} \right]$ .

$\frac{d}{dx}\left[ \frac{1}{\sqrt{x + 1}} \right] = -\frac{1}{2}(x + 1)^{-3/2}$ .

Differentiate $y = (3x^2 + 2x + 1)^5$ .

$y' = 5(3x^2 + 2x + 1)^4(6x + 2)$ .

Differentiate $q(r) = \sin^2(r)$ .

$q'(r) = 2\sin(r)\cos(r)$ .

Differentiate $y = (5x - 3)^6$ .

$y' = 6(5x - 3)^5(5)$ .

Find the derivative of $y = e^{-x^2}$ .

$y' = e^{-x^2}(-2x)$ .

Compute the derivative of $m(p) = \cosh(p^3)$ .

$m'(p) = \sinh(p^3)(3p^2)$ .

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