Calculus Examples

$y = x^{0.5}$

Step 1

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 0.5$ .

$0.5 x^{- 0.5}$

Step 2

Simplify.

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Step 2.1

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

$0.5 \frac{1}{x^{0.5}}$

Step 2.2

Combine $0.5$ and $\frac{1}{x^{0.5}}$ .

$\frac{0.5}{x^{0.5}}$