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Popular >

derivative of (x^5/5-1/2 x^{-2})

Solution

\frac{d}{d x} (\frac{x ^{5}}{5} - \frac{1}{2} x^{- 2})

Solution

x^{4} + \frac{1}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x ^{5}}{5} - \frac{1}{2} x^{- 2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{x ^{5}}{5}) - \frac{d}{d x} (\frac{1}{2} x^{- 2})

\frac{d}{d x} (\frac{x ^{5}}{5}) = x^{4}

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

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

Simplify

= x^{4} + \frac{1}{x ^{3}}

Popular Examples

derivative of 4/(x^2+4)derivative of

\frac{4}{x ^{2} + 4}

(dy)/(dx)=e^{-y}cos(x)

\frac{d y}{d x} = e^{- y} cos (x)

integral of 9sin^3(xco)s^2x

\int 9 sin^{3} (x co) s^{2} x d x

derivative of (2u^2)/((u^2+u)^3)derivative of

\frac{2 u ^{2}}{( u ^{2} + u ) ^{3}}

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

\int \frac{1}{( 3 x ) ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^5/5-1/2 x^{-2}) ?
The derivative of (x^5/5-1/2 x^{-2}) is x^4+1/(x^3)
What is the first derivative of (x^5/5-1/2 x^{-2}) ?
The first derivative of (x^5/5-1/2 x^{-2}) is x^4+1/(x^3)