Find the Derivative f(x)=x^5-3x^4

$f (x) = x^{5} - 3 x^{4}$

Differentiate.

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By the Sum Rule, the derivative of $x^{5} - 3 x^{4}$ with respect to $x$ is $\frac{d}{d x} [x^{5}] + \frac{d}{d x} [- 3 x^{4}]$ .

$\frac{d}{d x} [x^{5}] + \frac{d}{d x} [- 3 x^{4}]$

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 5$ .

$5 x^{4} + \frac{d}{d x} [- 3 x^{4}]$

Evaluate $\frac{d}{d x} [- 3 x^{4}]$ .

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Since $- 3$ is constant with respect to $x$ , the derivative of $- 3 x^{4}$ with respect to $x$ is $- 3 \frac{d}{d x} [x^{4}]$ .

$5 x^{4} - 3 \frac{d}{d x} [x^{4}]$

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

$5 x^{4} - 3 (4 x^{3})$

Multiply $4$ by $- 3$ .

$5 x^{4} - 12 x^{3}$

Find the Derivative f(x)=x^5-3x^4

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