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Popular >

derivative of 1/(x^7+2)

Solution

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

Solution

- \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}}

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\frac{\partial}{\partial x} (x^{2} + 2 x y)

integral of 3e^xsin(3x)

\int 3 e^{x} sin (3 x) d x

(\partial)/(\partial x)(sin(x)+y)

\frac{\partial}{\partial x} (sin (x) + y)

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\int 2 t 1 + t^{2} d t

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\int \frac{x}{( x ^{2} + 4 x + 13 ) ^{\frac{3}{2}}} d x

Frequently Asked Questions (FAQ)

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)