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Popular >

derivative of 1/(4x^3)

Solution

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

Solution

- \frac{3}{4 x ^{4}}

Solution steps

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

Take the constant out:

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

= \frac{1}{4} \frac{d}{d x} (\frac{1}{x ^{3}})

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

= - \frac{3}{4 x ^{4}}

Popular Examples

derivative of ln(x^3-1)

\frac{d}{d x} (ln (x^{3} - 1))

integral from-4 to 2 of (12-x-x^2)-(x+4)

\int_{- 4}^{2} (12 - x - x^{2}) - (x + 4) d x

(\partial)/(\partial x)(x^5+7x^5y)

\frac{\partial}{\partial x} (x^{5} + 7 x^{5} y)

limit as x approaches-4 of (x^2+3)/(x-1)

x \to - 4 lim (\frac{x ^{2} + 3}{x - 1})

e^yy^'+t/(y+1)= 2/(y+1)

e^{y} y^{^{'}} + \frac{t}{y + 1} = \frac{2}{y + 1}

Frequently Asked Questions (FAQ)

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