Composite, Implicit, and Inverse Functions

$\frac{x}{y}$

$-\frac{x}{y}$

$\frac{y}{x}$

$-\frac{y}{x}$

2cos(2x)

$cos(2x)$

$-2cos(2x)$

$-cos(2x)$

$\sin(x^2) + 2x^2cos(x^2)$

$\cos(x^2) + xcos(x^2)$

$\sin(x^2) + xcos(x^2)$

$\cos(x^2) + 2x^2\sin(x^2)$

Concave up when $f''(x) > 0$ and concave down when $f''(x) < 0$.

Concave up when $f''(x) < 0$ and concave down when $f''(x) > 0$.

Concave up when $f'(x) > 0$ and concave down when $f'(x) < 0$.

Concave up when $f'(x) < 0$ and concave down when $f'(x) > 0$.

$\frac{-2x}{\cos(y) - 1}$

$\frac{2x}{\cos(y) - 1}$

$\frac{-2x}{\cos(y) + 1}$

$\frac{2x}{\cos(y) + 1}$

6x - \sin(x)

6x + \sin(x)

3x^2 + \cos(x)

3x^2 - \cos(x)

$e^{-\sin(x)}$

$e^{\cos(x)}$

$e^{\cos(x)} \cdot \sin(x)$

$-e^{\cos(x)} \cdot \sin(x)$

$\frac{-25}{y^3}$

$\frac{25}{y^3}$

$\frac{x^2}{y^2}$

$\frac{-x^2}{y^2}$

$e^x(x+3)$

$e^x(x+1)$

$e^x(x+2)$

$e^x(x+4)$

2

2.5

3

5