What is the derivative of (x^2/(sqrt(x+1))) ?

The derivative of (x^2/(sqrt(x+1))) is (3x^2+4x)/(2(x+1)sqrt(x+1))

What is the first derivative of (x^2/(sqrt(x+1))) ?

The first derivative of (x^2/(sqrt(x+1))) is (3x^2+4x)/(2(x+1)sqrt(x+1))

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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

x \to - 1 lim (\frac{4 x - 5}{3 - x})

f (x) = x^{2} - x + 19, at x = 3

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

f (x) = (x - 1) (x - 3)^{2}, at x = 4

What is the derivative of (x^2/(sqrt(x+1))) ?
The derivative of (x^2/(sqrt(x+1))) is (3x^2+4x)/(2(x+1)sqrt(x+1))
What is the first derivative of (x^2/(sqrt(x+1))) ?
The first derivative of (x^2/(sqrt(x+1))) is (3x^2+4x)/(2(x+1)sqrt(x+1))