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Popular Calculus >

derivative of sqrt(x^3)+1/(sqrt(x))

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Graph

Popular Examples

derivative of 7e^xcos(x)

d er i v a t i v e 7 e^{x} cos (x)

integral of 1/(5x^5)

\int \frac{1}{5 x ^{5}} d x

integral from 0 to 8 of sqrt(64-x^2)

\int_{0}^{8} 64 - x^{2} d x

(x^2+1)((dy)/(dx))+8x(y-1)=0,y(0)=5

(x^{2} + 1) (\frac{d y}{d x}) + 8 x (y - 1) = 0, y (0) = 5

6 x + \frac{d y}{d x} = 0

Frequently Asked Questions (FAQ)

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