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}}}

y^{^{''}} + 4 y^{^{'}} + 5 y = 34 e^{2 t}, y (0) = 1, y^{^{'}} (0) = 2

y^{^{''}} = 32 e^{2 t}, y (0) = 3, y^{^{'}} (0) = 8

\int_{a}^{b} \frac{1}{b - a}

16 y^{^{''}} + 24 y^{^{'}} + 9 y = 0, y (2) = 4, y^{^{'}} (- 2) = - 3

- 3 cos (- 3 x)

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)}