What is the derivative of (sqrt(x)-5/(sqrt(x)+1)) ?

The derivative of (sqrt(x)-5/(sqrt(x)+1)) is 3/(sqrt(x)(\sqrt{x)+1)^2}

What is the first derivative of (sqrt(x)-5/(sqrt(x)+1)) ?

The first derivative of (sqrt(x)-5/(sqrt(x)+1)) is 3/(sqrt(x)(\sqrt{x)+1)^2}

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\frac{d}{d x} (\frac{x - 5}{x + 1})

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

Solution steps

\frac{d}{d x} (\frac{x - 5}{x + 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 5 ) ( x + 1 ) - \frac{d}{d x} ( x + 1 ) ( x - 5 )}{( x + 1 ) ^{2}}

\frac{d}{d x} (x - 5) = \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 - 5 )}{( x + 1 ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( x + 1 ) - \frac{1}{2 x} ( x - 5 )}{( x + 1 ) ^{2}} : \frac{3}{x ( x + 1 ) ^{2}}

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

\int tan (x) \cdot sec (x) d x

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

x^{4} - x^{5} y^{2} = - 3, (1, 2)

\frac{d}{d x} (- \frac{21}{x ^{4}})

\int x^{2} \cdot ln (x) d x

What is the derivative of (sqrt(x)-5/(sqrt(x)+1)) ?
The derivative of (sqrt(x)-5/(sqrt(x)+1)) is 3/(sqrt(x)(\sqrt{x)+1)^2}
What is the first derivative of (sqrt(x)-5/(sqrt(x)+1)) ?
The first derivative of (sqrt(x)-5/(sqrt(x)+1)) is 3/(sqrt(x)(\sqrt{x)+1)^2}