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Popular >

derivative of 1/(4x^2)

Solution

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

Solution

- \frac{1}{2 x ^{3}}

Solution steps

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

Take the constant out:

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

= \frac{1}{4} \frac{d}{d x} (\frac{1}{x ^{2}})

Apply exponent rule:

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

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

Apply the Power Rule:

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

= \frac{1}{4} (- 2 x^{- 2 - 1})

Simplify

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

= - \frac{1}{2 x ^{3}}

Popular Examples

derivative of (x^2-3/(x^2+1))

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integral from 1 to 5 of t^3ln(4t)

\int_{1}^{5} t^{3} ln (4 t) d t

integral of (x-1)/(x^2-2x+3)

\int \frac{x - 1}{x ^{2} - 2 x + 3} d x

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

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\frac{d}{d x} ((7 arcsin (4 x))^{x})

Frequently Asked Questions (FAQ)

What is the derivative of 1/(4x^2) ?
The derivative of 1/(4x^2) is -1/(2x^3)
What is the first derivative of 1/(4x^2) ?
The first derivative of 1/(4x^2) is -1/(2x^3)