Calculus Examples

$f (x) = \frac{1}{2} \cdot {(4 t + 3)}^{- \frac{1}{2}}$ , $x = 4$

Step 1

Find the derivative.

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Step 1.1

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

$\frac{d}{d x} [\frac{1}{2} \cdot \frac{1}{{(4 t + 3)}^{\frac{1}{2}}}]$

Step 1.2

Multiply $\frac{1}{2}$ by $\frac{1}{{(4 t + 3)}^{\frac{1}{2}}}$ .

$\frac{d}{d x} [\frac{1}{2 {(4 t + 3)}^{\frac{1}{2}}}]$

Step 1.3

Since $\frac{1}{2 {(4 t + 3)}^{\frac{1}{2}}}$ is constant with respect to $x$ , the derivative of $\frac{1}{2 {(4 t + 3)}^{\frac{1}{2}}}$ with respect to $x$ is $0$ .

$0$

Step 2

Replace the variable $x$ with $4$ in the expression.

$f' (4) = 0$