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Popular >

derivative of 1/({g(x)})

Solution

\frac{d}{d x} (\frac{1}{g ( x )})

Solution

- \frac{\frac{d}{d x} ( g ( x ) )}{g ( x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{g ( x )})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

Simplify

- \frac{1}{g ( x ) ^{2}} \frac{d}{d x} (g (x)) : - \frac{\frac{d}{d x} ( g ( x ) )}{g ( x ) ^{2}}

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

Popular Examples

integral of 8^{3x-1}

\int 8^{3 x - 1} d x

derivative of 24x-176 derivative of

24 x - 176

integral from 3 to 4 of 1/((x-3)^{3/2)}

\int_{3}^{4} \frac{1}{( x - 3 ) ^{\frac{3}{2}}} d x

integral of 1/(1-sin(5x))

\int \frac{1}{1 - sin ( 5 x )} d x

derivative of 16xsin(x)

\frac{d}{d x} (16 x sin (x))

Frequently Asked Questions (FAQ)

What is the derivative of 1/({g(x)}) ?
The derivative of 1/({g(x)}) is -(derivative of {g}(x))/({g)(x)^2}
What is the first derivative of 1/({g(x)}) ?
The first derivative of 1/({g(x)}) is -(derivative of {g}(x))/({g)(x)^2}