Find the Derivative - d/dx (x^3)/3-3x^2-7x

$\frac{x^{3}}{3} - 3 x^{2} - 7 x$

Step 1

By the Sum Rule, the derivative of $\frac{x^{3}}{3} - 3 x^{2} - 7 x$ with respect to $x$ is $\frac{d}{d x} [\frac{x^{3}}{3}] + \frac{d}{d x} [- 3 x^{2}] + \frac{d}{d x} [- 7 x]$ .

$\frac{d}{d x} [\frac{x^{3}}{3}] + \frac{d}{d x} [- 3 x^{2}] + \frac{d}{d x} [- 7 x]$

Step 2

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

Since $\frac{1}{3}$ is constant with respect to $x$ , the derivative of $\frac{x^{3}}{3}$ with respect to $x$ is $\frac{1}{3} \frac{d}{d x} [x^{3}]$ .

$\frac{1}{3} \frac{d}{d x} [x^{3}] + \frac{d}{d x} [- 3 x^{2}] + \frac{d}{d x} [- 7 x]$

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 3$ .

$\frac{1}{3} (3 x^{2}) + \frac{d}{d x} [- 3 x^{2}] + \frac{d}{d x} [- 7 x]$

Combine $3$ and $\frac{1}{3}$ .

$\frac{3}{3} x^{2} + \frac{d}{d x} [- 3 x^{2}] + \frac{d}{d x} [- 7 x]$

Combine $\frac{3}{3}$ and $x^{2}$ .

$\frac{3 x^{2}}{3} + \frac{d}{d x} [- 3 x^{2}] + \frac{d}{d x} [- 7 x]$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2}}{3} + \frac{d}{d x} [- 3 x^{2}] + \frac{d}{d x} [- 7 x]$

Divide $x^{2}$ by $1$ .

$x^{2} + \frac{d}{d x} [- 3 x^{2}] + \frac{d}{d x} [- 7 x]$

Step 3

Evaluate $\frac{d}{d x} [- 3 x^{2}]$ .

Since $- 3$ is constant with respect to $x$ , the derivative of $- 3 x^{2}$ with respect to $x$ is $- 3 \frac{d}{d x} [x^{2}]$ .

$x^{2} - 3 \frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 7 x]$

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

$x^{2} - 3 (2 x) + \frac{d}{d x} [- 7 x]$

Multiply $2$ by $- 3$ .

$x^{2} - 6 x + \frac{d}{d x} [- 7 x]$

Step 4

Evaluate $\frac{d}{d x} [- 7 x]$ .

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 x$ with respect to $x$ is $- 7 \frac{d}{d x} [x]$ .

$x^{2} - 6 x - 7 \frac{d}{d x} [x]$

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

$x^{2} - 6 x - 7 \cdot 1$

Multiply $- 7$ by $1$ .

$x^{2} - 6 x - 7$

Find the Derivative - d/dx (x^3)/3-3x^2-7x

Related Questions

Support LCMGCF.com by disabling your adblocker.