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Popular >

derivative of 1/(x^2+1/(x^6))

Solution

\frac{d}{d x} (\frac{1}{x ^{2}} + \frac{1}{x ^{6}})

Solution

- \frac{2}{x ^{3}} - \frac{6}{x ^{7}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{2}} + \frac{1}{x ^{6}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{1}{x ^{2}}) + \frac{d}{d x} (\frac{1}{x ^{6}})

\frac{d}{d x} (\frac{1}{x ^{2}}) = - \frac{2}{x ^{3}}

\frac{d}{d x} (\frac{1}{x ^{6}}) = - \frac{6}{x ^{7}}

= - \frac{2}{x ^{3}} - \frac{6}{x ^{7}}

Popular Examples

derivative of (3x^4/5)

\frac{d}{d x} (\frac{3 x ^{4}}{5})

inverse oflaplace s/(s^2+6s+10)inverse laplace

\frac{s}{s ^{2} + 6 s + 10}

y^{''}+7y^'=0,y(0)=-5,y^'(0)=-21

y^{^{''}} + 7 y^{^{'}} = 0, y (0) = - 5, y^{^{'}} (0) = - 21

integral of 3sqrt(x)e^{sqrt(x)}

\int 3 x e^{x} d x

integral of 1/(16e^{-2x)+e^{2x}}

\int \frac{1}{16 e ^{- 2 x} + e ^{2 x}} d x

Frequently Asked Questions (FAQ)

What is the derivative of 1/(x^2+1/(x^6)) ?
The derivative of 1/(x^2+1/(x^6)) is -2/(x^3)-6/(x^7)
What is the first derivative of 1/(x^2+1/(x^6)) ?
The first derivative of 1/(x^2+1/(x^6)) is -2/(x^3)-6/(x^7)