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

The derivative of 1/(g(x^2)) is -1/(g^2x^2)

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

The first derivative of 1/(g(x^2)) is -1/(g^2x^2)

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derivative of

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

- \frac{1}{g ^{2} x ^{2}}

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

= - \frac{1}{g ^{2} x ^{2}}

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

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