Find dy/dx y=2x^4-10x^2+13

$y = 2 x^{4} - 10 x^{2} + 13$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d x} (y) = \frac{d}{d x} (2 x^{4} - 10 x^{2} + 13)$

Step 2

The derivative of $y$ with respect to $x$ is $y'$ .

$y'$

Step 3

Differentiate the right side of the equation.

By the Sum Rule, the derivative of $2 x^{4} - 10 x^{2} + 13$ with respect to $x$ is $\frac{d}{d x} [2 x^{4}] + \frac{d}{d x} [- 10 x^{2}] + \frac{d}{d x} [13]$ .

$\frac{d}{d x} [2 x^{4}] + \frac{d}{d x} [- 10 x^{2}] + \frac{d}{d x} [13]$

Evaluate $\frac{d}{d x} [2 x^{4}]$ .

Since $2$ is constant with respect to $x$ , the derivative of $2 x^{4}$ with respect to $x$ is $2 \frac{d}{d x} [x^{4}]$ .

$2 \frac{d}{d x} [x^{4}] + \frac{d}{d x} [- 10 x^{2}] + \frac{d}{d x} [13]$

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 4$ .

$2 (4 x^{3}) + \frac{d}{d x} [- 10 x^{2}] + \frac{d}{d x} [13]$

Multiply $4$ by $2$ .

$8 x^{3} + \frac{d}{d x} [- 10 x^{2}] + \frac{d}{d x} [13]$

Evaluate $\frac{d}{d x} [- 10 x^{2}]$ .

Since $- 10$ is constant with respect to $x$ , the derivative of $- 10 x^{2}$ with respect to $x$ is $- 10 \frac{d}{d x} [x^{2}]$ .

$8 x^{3} - 10 \frac{d}{d x} [x^{2}] + \frac{d}{d x} [13]$

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

$8 x^{3} - 10 (2 x) + \frac{d}{d x} [13]$

Multiply $2$ by $- 10$ .

$8 x^{3} - 20 x + \frac{d}{d x} [13]$

Differentiate using the Constant Rule.

Since $13$ is constant with respect to $x$ , the derivative of $13$ with respect to $x$ is $0$ .

$8 x^{3} - 20 x + 0$

Add $8 x^{3} - 20 x$ and $0$ .

$8 x^{3} - 20 x$

Step 4

Reform the equation by setting the left side equal to the right side.

$y' = 8 x^{3} - 20 x$

Step 5

Replace $y'$ with $\frac{d y}{d x}$ .

$\frac{d y}{d x} = 8 x^{3} - 20 x$

Find dy/dx y=2x^4-10x^2+13

Related Questions

Support LCMGCF.com by disabling your adblocker.