Calculus Examples

$y = m x^{4}$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d x} (y) = \frac{d}{d x} (m x^{4})$

Step 2

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

$y'$

Step 3

Differentiate the right side of the equation.

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Step 3.1

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

$m \frac{d}{d x} [x^{4}]$

Step 3.2

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

$m (4 x^{3})$

Step 3.3

Reorder.

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Step 3.3.1

Move $4$ to the left of $m$ .

$4 \cdot m x^{3}$

Step 3.3.2

Reorder the factors of $4 m x^{3}$ .

$4 x^{3} m$

Step 4

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

$y' = 4 x^{3} m$

Step 5

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

$\frac{d y}{d x} = 4 x^{3} m$