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

The derivative of f(x)= 1/((2x^2)) is -1/(x^3)

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

The first derivative of f(x)= 1/((2x^2)) is -1/(x^3)

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derivative of

f (x) = \frac{1}{( 2 x ^{2} )}

- \frac{1}{x ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

= - \frac{1}{x ^{3}}

e^{- 5} x

f (x) = - 2 x^{2} - 5

cosh^{2} (x)

3 x^{2} + 5 x - 2

lo g_{10} (x^{2} - 1)

What is the derivative of f(x)= 1/((2x^2)) ?
The derivative of f(x)= 1/((2x^2)) is -1/(x^3)
What is the first derivative of f(x)= 1/((2x^2)) ?
The first derivative of f(x)= 1/((2x^2)) is -1/(x^3)