Calculus Examples

$\frac{d (5 x^{2} - 3 x)}{d x}$

Step 1

This derivative could not be completed using the chain rule. Mathway will use another method.

Step 2

By the Sum Rule, the derivative of $5 x^{2} - 3 x$ with respect to $x$ is $\frac{d}{d x} [5 x^{2}] + \frac{d}{d x} [- 3 x]$ .

$\frac{d}{d x} [5 x^{2}] + \frac{d}{d x} [- 3 x]$

Step 3

Evaluate $\frac{d}{d x} [5 x^{2}]$ .

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Step 3.1

Since $5$ is constant with respect to $x$ , the derivative of $5 x^{2}$ with respect to $x$ is $5 \frac{d}{d x} [x^{2}]$ .

$5 \frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 3 x]$

Step 3.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$5 (2 x) + \frac{d}{d x} [- 3 x]$

Step 3.3

Multiply $2$ by $5$ .

$10 x + \frac{d}{d x} [- 3 x]$

Step 4

Evaluate $\frac{d}{d x} [- 3 x]$ .

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Step 4.1

Since $- 3$ is constant with respect to $x$ , the derivative of $- 3 x$ with respect to $x$ is $- 3 \frac{d}{d x} [x]$ .

$10 x - 3 \frac{d}{d x} [x]$

Step 4.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 1$ .

$10 x - 3 \cdot 1$

Step 4.3

Multiply $- 3$ by $1$ .

$10 x - 3$