Calculus Examples

$f (t) = t^{- 4}$ ;, $(\frac{1}{2}, 16)$

Step 1

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

$y = \frac{1}{t^{4}}$

Step 2

Find the derivative of the function. To find the slope of the equation tangent to the line, evaluate the derivative at the desired value of $x$ .

$\frac{d}{d x} (t^{- 4})$

Step 3

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

$\frac{d}{d x} [\frac{1}{t^{4}}]$

Step 4

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

$0$

Step 5

The derivative of the equation in terms of $y$ can also be represented as $f' (x)$ .

$f' (x) = 0$

Step 6

Replace the variable $x$ with $\frac{1}{2}$ in the expression.

$f' (\frac{1}{2}) = 0$

Step 7

The derivative at $(\frac{1}{2}, 16)$ is $0$ .

$0$