What is the derivative of (x^2/(7+sqrt(x))) ?

The derivative of (x^2/(7+sqrt(x))) is (4x(7+sqrt(x))-x^{3/2})/(2(7+sqrt(x))^2)

What is the first derivative of (x^2/(7+sqrt(x))) ?

The first derivative of (x^2/(7+sqrt(x))) is (4x(7+sqrt(x))-x^{3/2})/(2(7+sqrt(x))^2)

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\frac{d}{d x} (\frac{x ^{2}}{7 + x})

\frac{4 x ( 7 + x ) - x ^{\frac{3}{2}}}{2 ( 7 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{7 + x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 7 + x ) - \frac{d}{d x} ( 7 + x ) x ^{2}}{( 7 + x ) ^{2}}

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

\frac{d}{d x} (7 + x) = \frac{1}{2 x}

= \frac{2 x ( 7 + x ) - \frac{1}{2 x} x ^{2}}{( 7 + x ) ^{2}}

Simplify

\frac{2 x ( 7 + x ) - \frac{1}{2 x} x ^{2}}{( 7 + x ) ^{2}} : \frac{4 x ( 7 + x ) - x ^{\frac{3}{2}}}{2 ( 7 + x ) ^{2}}

= \frac{4 x ( 7 + x ) - x ^{\frac{3}{2}}}{2 ( 7 + x ) ^{2}}

\int_{- \infty}^{0} \frac{1}{2 - 4 x} d x

\int_{a}^{b} f (x) d x

(ln (\frac{x}{4}))^{^{'}}

\int 2 x (2 - x) d x

3^{2^{x^{2}}}

What is the derivative of (x^2/(7+sqrt(x))) ?
The derivative of (x^2/(7+sqrt(x))) is (4x(7+sqrt(x))-x^{3/2})/(2(7+sqrt(x))^2)
What is the first derivative of (x^2/(7+sqrt(x))) ?
The first derivative of (x^2/(7+sqrt(x))) is (4x(7+sqrt(x))-x^{3/2})/(2(7+sqrt(x))^2)