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Popular >

derivative of 3/(4x^3)

Solution

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

Solution

- \frac{9}{4 x ^{4}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

\frac{3}{4} (- 3 x^{- 3 - 1}) : - \frac{9}{4 x ^{4}}

= - \frac{9}{4 x ^{4}}

Popular Examples

integral from 0 to 3 of sqrt(x^2-9)

\int_{0}^{3} x^{2} - 9 d x

integral of 30+(60)/(e^{0.06x)}

\int 30 + \frac{60}{e ^{0.06 x}} d x

\frac{d}{d y} (6 x y)

integral of 1/(xsqrt(a^2-a^2x^2))

\int \frac{1}{x a ^{2} - a ^{2} x ^{2}} d x

(dy)/(dx)=((y^3))/(x^2)

\frac{d y}{d x} = \frac{( y ^{3} )}{x ^{2}}

Frequently Asked Questions (FAQ)

What is the derivative of 3/(4x^3) ?
The derivative of 3/(4x^3) is -9/(4x^4)
What is the first derivative of 3/(4x^3) ?
The first derivative of 3/(4x^3) is -9/(4x^4)