Calculus Examples

$q (x) = \frac{895 + \sqrt{10}}{x}$

Step 1

Since $895 + \sqrt{10}$ is constant with respect to $x$ , the derivative of $\frac{895 + \sqrt{10}}{x}$ with respect to $x$ is $(895 + \sqrt{10}) \frac{d}{d x} [\frac{1}{x}]$ .

$(895 + \sqrt{10}) \frac{d}{d x} [\frac{1}{x}]$

Step 2

Rewrite $\frac{1}{x}$ as $x^{- 1}$ .

$(895 + \sqrt{10}) \frac{d}{d x} [x^{- 1}]$

Step 3

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

$(895 + \sqrt{10}) (- x^{- 2})$

Step 4

Simplify.

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Step 4.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(895 + \sqrt{10}) (- \frac{1}{x^{2}})$

Step 4.2

Apply the distributive property.

$895 (- \frac{1}{x^{2}}) + \sqrt{10} (- \frac{1}{x^{2}})$

Step 4.3

Combine terms.

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Step 4.3.1

Multiply $- 1$ by $895$ .

$- 895 \frac{1}{x^{2}} + \sqrt{10} (- \frac{1}{x^{2}})$

Step 4.3.2

Combine $- 895$ and $\frac{1}{x^{2}}$ .

$\frac{- 895}{x^{2}} + \sqrt{10} (- \frac{1}{x^{2}})$

Step 4.3.3

Move the negative in front of the fraction.

$- \frac{895}{x^{2}} + \sqrt{10} (- \frac{1}{x^{2}})$

Step 4.3.4

Combine $\sqrt{10}$ and $\frac{1}{x^{2}}$ .

$- \frac{895}{x^{2}} - \frac{\sqrt{10}}{x^{2}}$