What is the derivative of sqrt((5x+1/(x^2-3))) ?

The derivative of sqrt((5x+1/(x^2-3))) is (-5x^2-2x-15)/(2sqrt(5x+1)(x^2-3)^{3/2)}

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

The first derivative of sqrt((5x+1/(x^2-3))) is (-5x^2-2x-15)/(2sqrt(5x+1)(x^2-3)^{3/2)}

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

\frac{- 5 x ^{2} - 2 x - 15}{2 5 x + 1 ( x ^{2} - 3 ) ^{\frac{3}{2}}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{5 x + 1}{x ^{2} - 3}) = \frac{- 5 x ^{2} - 2 x - 15}{( x ^{2} - 3 ) ^{2}}

= \frac{1}{2 \frac{5 x + 1}{x ^{2} - 3}} \cdot \frac{- 5 x ^{2} - 2 x - 15}{( x ^{2} - 3 ) ^{2}}

Simplify

\frac{1}{2 \frac{5 x + 1}{x ^{2} - 3}} \cdot \frac{- 5 x ^{2} - 2 x - 15}{( x ^{2} - 3 ) ^{2}} : \frac{- 5 x ^{2} - 2 x - 15}{2 5 x + 1 ( x ^{2} - 3 ) ^{\frac{3}{2}}}

= \frac{- 5 x ^{2} - 2 x - 15}{2 5 x + 1 ( x ^{2} - 3 ) ^{\frac{3}{2}}}

\int sin^{4} (x) \cdot cos^{7} (x) d x

\frac{\partial}{\partial y} (x^{2} + y^{2} - 2 x)

\int cot (48 x) d x

\frac{d}{d x} (e^{c o s (2 x)} \cdot sin (2 x))

x \to \infty lim (xxxxx)

What is the derivative of sqrt((5x+1/(x^2-3))) ?
The derivative of sqrt((5x+1/(x^2-3))) is (-5x^2-2x-15)/(2sqrt(5x+1)(x^2-3)^{3/2)}
What is the first derivative of sqrt((5x+1/(x^2-3))) ?
The first derivative of sqrt((5x+1/(x^2-3))) is (-5x^2-2x-15)/(2sqrt(5x+1)(x^2-3)^{3/2)}