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Popular >

derivative of 1/(2z^3)

Solution

derivative of

\frac{1}{2 z ^{3}}

Solution

- \frac{3}{2 z ^{4}}

Solution steps

\frac{d}{d z} (\frac{1}{2 z ^{3}})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d z} (\frac{1}{z ^{3}})

Apply exponent rule:

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

= \frac{1}{2} \frac{d}{d z} (z^{- 3})

Apply the Power Rule:

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

= \frac{1}{2} (- 3 z^{- 3 - 1})

Simplify

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

= - \frac{3}{2 z ^{4}}

Popular Examples

y^'=-(2y)/(x+1)+2x

y^{^{'}} = - \frac{2 y}{x + 1} + 2 x

limit as x approaches 4 of x^2-1

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

integral of xln^5(x)

\int x ln^{5} (x) d x

derivative of f(x)=x^4sin(4x)derivative of

f (x) = x^{4} sin (4 x)

integral from 1 to 2 of 1

\int_{1}^{2} 1

Frequently Asked Questions (FAQ)

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