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

The derivative of f(x)=(x^2)/(3+sqrt(x)) is (4x(3+sqrt(x))-x^{3/2})/(2(3+sqrt(x))^2)

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

The first derivative of f(x)=(x^2)/(3+sqrt(x)) is (4x(3+sqrt(x))-x^{3/2})/(2(3+sqrt(x))^2)

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derivative of

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

\frac{4 x ( 3 + x ) - x ^{\frac{3}{2}}}{2 ( 3 + x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{4 x ( 3 + x ) - x ^{\frac{3}{2}}}{2 ( 3 + x ) ^{2}}

\frac{d y}{d x} = 8 y e^{x + 2}

\int \frac{1}{t ^{3} + t ^{2} - 2 t} d t

\int \frac{32 x ^{2}}{( x - 15 ) ( x + 5 ) ^{2}} d x

\int 8^{- x} d x

\frac{d}{d x} (\frac{1}{sec ^{2} ( 4 x )})

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