Calculus Examples

$\frac{\sqrt{5}}{t^{6}}$

Step 1

Since $\sqrt{5}$ is constant with respect to $t$ , the derivative of $\frac{\sqrt{5}}{t^{6}}$ with respect to $t$ is $\sqrt{5} \frac{d}{d t} [\frac{1}{t^{6}}]$ .

$\sqrt{5} \frac{d}{d t} [\frac{1}{t^{6}}]$

Step 2

Apply basic rules of exponents.

Tap for more steps...

Step 2.1

Rewrite $\frac{1}{t^{6}}$ as ${(t^{6})}^{- 1}$ .

$\sqrt{5} \frac{d}{d t} [{(t^{6})}^{- 1}]$

Step 2.2

Multiply the exponents in ${(t^{6})}^{- 1}$ .

Tap for more steps...

Step 2.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\sqrt{5} \frac{d}{d t} [t^{6 \cdot - 1}]$

Step 2.2.2

Multiply $6$ by $- 1$ .

$\sqrt{5} \frac{d}{d t} [t^{- 6}]$

Step 3

Differentiate using the Power Rule which states that $\frac{d}{d t} [t^{n}]$ is $n t^{n - 1}$ where $n = - 6$ .

$\sqrt{5} (- 6 t^{- 7})$

Step 4

Simplify.

Tap for more steps...

Step 4.1

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

$\sqrt{5} (- 6 \frac{1}{t^{7}})$

Step 4.2

Combine terms.

Tap for more steps...

Step 4.2.1

Combine $- 6$ and $\frac{1}{t^{7}}$ .

$\sqrt{5} \frac{- 6}{t^{7}}$

Step 4.2.2

Move the negative in front of the fraction.

$\sqrt{5} (- \frac{6}{t^{7}})$

Step 4.2.3

Combine $\sqrt{5}$ and $\frac{6}{t^{7}}$ .

$- \frac{\sqrt{5} \cdot 6}{t^{7}}$

Step 4.2.4

Move $6$ to the left of $\sqrt{5}$ .

$- \frac{6 \sqrt{5}}{t^{7}}$