Calculus Examples

$y = x^{2} + 1 (\cot (x))$

Differentiate.

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By the Sum Rule, the derivative of $x^{2} + 1 (\cot (x))$ with respect to $x$ is $\frac{d}{d x} [x^{2}] + \frac{d}{d x} [1 (\cot (x))]$ .

$\frac{d}{d x} [x^{2}] + \frac{d}{d x} [1 (\cot (x))]$

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

$2 x + \frac{d}{d x} [1 (\cot (x))]$

Evaluate $\frac{d}{d x} [1 (\cot (x))]$ .

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Multiply $\cot (x)$ by $1$ .

$2 x + \frac{d}{d x} [\cot (x)]$

The derivative of $\cot (x)$ with respect to $x$ is $- \csc^{2} (x)$ .

$2 x - \csc^{2} (x)$