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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x^{3} + x^{2} + x + 1

\int cos (5 x) sin (3 x) d x

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

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

\frac{d}{d x} (\frac{375}{x ^{4}})

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