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}}

x \to 0 lim (x^{2} \cdot cos (\frac{1}{x}))

\int \frac{1}{5 x + 7} d x

\int_{0}^{1} sin^{2} (2 π x) d x

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

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

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)