What is the derivative of (xsqrt(x+1)/(x+1)) ?

The derivative of (xsqrt(x+1)/(x+1)) is (x+2)/(2(x+1)^{3/2)}

What is the first derivative of (xsqrt(x+1)/(x+1)) ?

The first derivative of (xsqrt(x+1)/(x+1)) is (x+2)/(2(x+1)^{3/2)}

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

y^{^{'}} + 6 y = e^{t}

\int \frac{5}{3 - 2 cos ( x )} d x

x \to 3 lim (4 π)

\frac{\partial}{\partial x} (x cos (\frac{y}{z}))

\frac{d}{d x} (x + e^{- x})

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