Find the Derivative Using Quotient Rule - d/dm m=8/(n^7)

$m = \frac{8}{n^{7}}$

Step 1

Differentiate using the Quotient Rule which states that $\frac{d}{d m} [\frac{f (m)}{g (m)}]$ is $\frac{g (m) \frac{d}{d m} [f (m)] - f (m) \frac{d}{d m} [g (m)]}{{g (m)}^{2}}$ where $f (m) = 8$ and $g (m) = n^{7}$ .

$\frac{n^{7} \frac{d}{d m} [8] - 1 \cdot 8 \frac{d}{d m} [n^{7}]}{{(n^{7})}^{2}}$

Step 2

Differentiate using the Constant Rule.

Since $8$ is constant with respect to $m$ , the derivative of $8$ with respect to $m$ is $0$ .

$\frac{n^{7} \cdot 0 - 1 \cdot 8 \frac{d}{d m} [n^{7}]}{{(n^{7})}^{2}}$

Since $n^{7}$ is constant with respect to $m$ , the derivative of $n^{7}$ with respect to $m$ is $0$ .

$\frac{n^{7} \cdot 0 - 1 \cdot 8 \cdot 0}{{(n^{7})}^{2}}$

Step 3

Simplify.

Simplify the numerator.

Simplify each term.

Multiply $n^{7}$ by $0$ .

$\frac{0 - 1 \cdot 8 \cdot 0}{{(n^{7})}^{2}}$

Multiply $- 1 \cdot 8 \cdot 0$ .

Multiply $- 1$ by $8$ .

$\frac{0 - 8 \cdot 0}{{(n^{7})}^{2}}$

Multiply $- 8$ by $0$ .

$\frac{0 + 0}{{(n^{7})}^{2}}$

Add $0$ and $0$ .

$\frac{0}{{(n^{7})}^{2}}$

Multiply the exponents in ${(n^{7})}^{2}$ .

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

$\frac{0}{n^{7 \cdot 2}}$

Multiply $7$ by $2$ .

$\frac{0}{n^{14}}$

Divide $0$ by $n^{14}$ .

$0$

Find the Derivative Using Quotient Rule - d/dm m=8/(n^7)

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