Find dy/dx y=10x^9-4x

$y = 10 x^{9} - 4 x$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d x} (y) = \frac{d}{d x} (10 x^{9} - 4 x)$

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 $10 x^{9} - 4 x$ with respect to $x$ is $\frac{d}{d x} [10 x^{9}] + \frac{d}{d x} [- 4 x]$ .

$\frac{d}{d x} [10 x^{9}] + \frac{d}{d x} [- 4 x]$

Evaluate $\frac{d}{d x} [10 x^{9}]$ .

Since $10$ is constant with respect to $x$ , the derivative of $10 x^{9}$ with respect to $x$ is $10 \frac{d}{d x} [x^{9}]$ .

$10 \frac{d}{d x} [x^{9}] + \frac{d}{d x} [- 4 x]$

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 9$ .

$10 (9 x^{8}) + \frac{d}{d x} [- 4 x]$

Multiply $9$ by $10$ .

$90 x^{8} + \frac{d}{d x} [- 4 x]$

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

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

$90 x^{8} - 4 \frac{d}{d x} [x]$

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

$90 x^{8} - 4 \cdot 1$

Multiply $- 4$ by $1$ .

$90 x^{8} - 4$

Step 4

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

$y' = 90 x^{8} - 4$

Step 5

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

$\frac{d y}{d x} = 90 x^{8} - 4$