Composite, Implicit, and Inverse Functions

$-\sin(3x)$

$-3\cos(3x)$

$-3\sin(3x)$

$-\cos(3x)$

$\Delta f(4)$

$\frac{d}{dx} f(4)$

$\int f(4) dx$

$f'(4)$

$\int_a^b |f(x)| ,dx$

$\int_a^b f'(x) ,dx$

$\sum_{x=a}^{b} f(x)\Delta x$

$\int_a^b f(x) ,dx$

$e^{2x}$

$2e^{2x + 3}$

$e^{2x + 3}$

$2e^{2x}$

$12x^3 + 4x^2 - 6x$

$12x^3 + 4x^2 + 6x$

$12x^2 + 4x + 6$

$12x^2 + 4x - 6$

-tan(x)

-1/(sin(x))

-1/(cos(x))

-cot(x)

$f'(x) = e^{3g(x)}$

$f'(x) = 3e^{g(x)}$

$f'(x) = g''(x)e^{g(x)}$

$f'(x) = g'(x)e^{g(x)}$

5e^x + 2/x

5e^x - 1/x

5e^x + 1/x

5e^x - 2/x

$5$

$-3$

Does not exist.

$0$

$\frac{1}{3}x^{-2/3} + x^{-1/2}$

$\frac{1}{3}x^{2/3} + \frac{1}{2}x^{1/2}$

$\frac{1}{3}x^{2/3} + x^{1/2}$

$\frac{1}{3}x^{-2/3} + \frac{1}{2}x^{-1/2}$