Fundamentals of Differentiation

$\frac{dw}{dv}=\frac{w}{e}$

$\frac{dw}{dv}=\frac{e}{w}$

$\frac{dw}{dv}=\frac{ev^2}{w^3}$

$\frac{dw}{dv}=\frac{v}{e}$

$p'(c) = -\frac{q'(c)}{\ln(c)}$

$p'(c) = \frac{q(c)}{c}$

$p'(c) = cq'(c)$

$p'(c) = -cq'(c)$

$\frac{4(3-x)}{(2-x)^3}$

$\frac{8(2+x)}{(2-x)^3}$

$\frac{-12}{(2-x)^4}$

$\frac{-8}{(2-x)^3}$

$f'(x) = \frac{\cos{x} - x\sin{x}}{x^3}$

$f'(x) = \frac{x^2\cos{x} - 2x\sin{x}}{x^4}$

$f'(x) = \frac{x^2\cos{x} + 2x\sin{x}}{x^4}$

$f'(x) = \frac{\cos{x}}{2x^3}$

$\frac{4x^5 - 9x^4 + 4x^3 - 4x}{(x^4 + 1)^2}$

$\frac{4x^5 - 9x^4 + 4x^3 - 4x + 3}{(2x^2 - 3x + 1)^2}$

$\frac{4x^5 - 9x^4 + 4x^3 - 4x + 3}{2x^2 - 3x + 1}$

$\frac{4x^5 - 9x^4 + 4x^3 - 4x + 3}{(x^4 + 1)^2}$

$\alpha = 0$

$\alpha = -e$

$\alpha = e$

$\alpha = \pi$

$\frac{-x^4 - 2x}{(x^3 + 1)^2}$

$\frac{x^4 + 2x}{(x^3 + 1)^2}$

$\frac{-x^4 + 2x}{(x^3 + 1)^2}$

$\frac{x^4 - 2x}{(x^3 + 1)^2}$

$1$

$-2$

$0$

Does not exist

Multiply $\frac{t}{\sqrt{t}}$ by $\frac{1}{2\sqrt{t}}$

Subtract $\frac{t}{\sqrt{t}} + t$ from $\sqrt{t}$

Subtract $\frac{t}{\sqrt{t}}$ from $\frac{1}{t}\sqrt{t}$

Divide $\frac{t}{\sqrt{t}}$ by $\sqrt{t}$

$-\frac{524288}{\pi^2}$

$-\frac{108576}{i}$

$\frac{104857}{\pi}$

$-\frac{524288}{\pi}$