What is the derivative of (sqrt(x)-3/(sqrt(x)+1)) ?

The derivative of (sqrt(x)-3/(sqrt(x)+1)) is 2/(sqrt(x)(\sqrt{x)+1)^2}

What is the first derivative of (sqrt(x)-3/(sqrt(x)+1)) ?

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

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\frac{d}{d x} (\frac{x - 3}{x + 1})

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

Solution steps

\frac{d}{d x} (\frac{x - 3}{x + 1})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

f (x) = \frac{1}{x ^{3}}, (1, 1)

\int sin^{2} (10 x) d x

\int (x + 3) (2 x - 1) d x

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

\int x \cdot (4 - x^{2})^{- \frac{2}{3}} d x

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