What is the derivative of (sqrt(x)+x^3/(x^2)) ?

The derivative of (sqrt(x)+x^3/(x^2)) is (2x^3-3sqrt(x))/(2x^3)

What is the first derivative of (sqrt(x)+x^3/(x^2)) ?

The first derivative of (sqrt(x)+x^3/(x^2)) is (2x^3-3sqrt(x))/(2x^3)

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

\frac{( \frac{1}{2 x} + 3 x ^{2} ) x ^{2} - 2 x ( x + x ^{3} )}{( x ^{2} ) ^{2}} : \frac{2 x ^{3} - 3 x}{2 x ^{3}}

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

x 18 - x^{2}

t e^{3 t}

f (x) = \frac{1}{x - 8}, (- 1, - \frac{1}{9})

\frac{d}{d x} (e^{- 3 x} cos (2 x))

\int \frac{9}{25 + 16 r ^{2}} d r

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