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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derivative of

\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}}}

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)}