Mathematical Functions and Their Derivatives

Flashcards providing the derivatives for various algebraic and power functions based on the lecture transcript.

$$2x^2+1$$

The derivative with respect to $x$ is $4x$.

$$2-\sqrt{\sqrt{x}}$$

The derivative with respect to $x$ is $-\frac{1}{4}x^{-3/4}$.

$$\frac{1}{x}$$

The derivative with respect to $x$ is $-\frac{1}{x^2}$.

$$\frac{1}{x^2}$$

The derivative with respect to $x$ is $-\frac{2}{x^3}$.

$$x(x-3)$$

The derivative with respect to $x$ is $2x-3$.

$$\frac{1}{x-a}$$

The derivative with respect to $x$ is $-\frac{1}{(x-a)^2}$.

$$(x+4)^3$$

The derivative with respect to $x$ is $3(x+4)^2$.

$$x^{3/2}$$

The derivative with respect to $x$ is $\frac{3}{2}x^{1/2}$.

$$x^n, n \in N$$

The derivative with respect to $x$ is $nx^{n-1}$.

$$\frac{1}{x^m}, m \in N$$

The derivative with respect to $x$ is $-\frac{m}{x^{m+1}}$.

$$x^{40}$$

The derivative with respect to $x$ is $40x^{39}$.

$$x^{-100}$$

The derivative with respect to $x$ is $-100x^{-101}$.