What is the derivative of 1/(x^7+2) ?

The derivative of 1/(x^7+2) is -(7x^6)/((x^7+2)^2)

What is the first derivative of 1/(x^7+2) ?

The first derivative of 1/(x^7+2) is -(7x^6)/((x^7+2)^2)

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\frac{d}{d x} (\frac{1}{x ^{7} + 2})

- \frac{7 x ^{6}}{( x ^{7} + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{7} + 2})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((x^{7} + 2)^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{7} + 2 ) ^{2}} \frac{d}{d x} (x^{7} + 2)

= - \frac{1}{( x ^{7} + 2 ) ^{2}} \frac{d}{d x} (x^{7} + 2)

\frac{d}{d x} (x^{7} + 2) = 7 x^{6}

= - \frac{1}{( x ^{7} + 2 ) ^{2}} \cdot 7 x^{6}

Simplify

- \frac{1}{( x ^{7} + 2 ) ^{2}} \cdot 7 x^{6} : - \frac{7 x ^{6}}{( x ^{7} + 2 ) ^{2}}

= - \frac{7 x ^{6}}{( x ^{7} + 2 ) ^{2}}

What is the derivative of 1/(x^7+2) ?
The derivative of 1/(x^7+2) is -(7x^6)/((x^7+2)^2)
What is the first derivative of 1/(x^7+2) ?
The first derivative of 1/(x^7+2) is -(7x^6)/((x^7+2)^2)