Calculus Examples

$t = 0.0588 s^{1.125}$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d s} (t) = \frac{d}{d s} (0.0588 s^{1.125})$

Step 2

The derivative of $t$ with respect to $s$ is $t'$ .

$t'$

Step 3

Differentiate the right side of the equation.

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Step 3.1

Since $0.0588$ is constant with respect to $s$ , the derivative of $0.0588 s^{1.125}$ with respect to $s$ is $0.0588 \frac{d}{d s} [s^{1.125}]$ .

$0.0588 \frac{d}{d s} [s^{1.125}]$

Step 3.2

Differentiate using the Power Rule which states that $\frac{d}{d s} [s^{n}]$ is $n s^{n - 1}$ where $n = 1.125$ .

$0.0588 (1.125 s^{0.125})$

Step 3.3

Multiply $1.125$ by $0.0588$ .

$0.06615 s^{0.125}$

Step 4

Reform the equation by setting the left side equal to the right side.

$t' = 0.06615 s^{0.125}$

Step 5

Replace $t'$ with $\frac{d t}{d s}$ .

$\frac{d t}{d s} = 0.06615 s^{0.125}$