Calculus Examples

$x^{3} {(1 - 4)}^{4}$

Step 1

Simplify the expression.

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Step 1.1

Subtract $4$ from $1$ .

$\frac{d}{d x} [x^{3} {(- 3)}^{4}]$

Step 1.2

Raise $- 3$ to the power of $4$ .

$\frac{d}{d x} [x^{3} \cdot 81]$

Step 1.3

Move $81$ to the left of $x^{3}$ .

$\frac{d}{d x} [81 \cdot x^{3}]$

Step 2

Since $81$ is constant with respect to $x$ , the derivative of $81 x^{3}$ with respect to $x$ is $81 \frac{d}{d x} [x^{3}]$ .

$81 \frac{d}{d x} [x^{3}]$

Step 3

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

$81 (3 x^{2})$

Step 4

Multiply $3$ by $81$ .

$243 x^{2}$