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

The derivative of (sqrt(x+1)/(x^2-5)) is (-3x^2-4x-5)/(2(x^2-5)^2sqrt(x+1))

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

The first derivative of (sqrt(x+1)/(x^2-5)) is (-3x^2-4x-5)/(2(x^2-5)^2sqrt(x+1))

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

\frac{- 3 x ^{2} - 4 x - 5}{2 ( x ^{2} - 5 ) ^{2} x + 1}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{\frac{1}{2 x + 1} ( x ^{2} - 5 ) - 2 x x + 1}{( x ^{2} - 5 ) ^{2}} : \frac{- 3 x ^{2} - 4 x - 5}{2 ( x ^{2} - 5 ) ^{2} x + 1}

= \frac{- 3 x ^{2} - 4 x - 5}{2 ( x ^{2} - 5 ) ^{2} x + 1}

f (x) = \frac{sin ( x ) - cos ( x )}{sin ( x ) + cos ( x )}

\int (2 x - 4)^{2} d x

y^{^{''}} + 4 y = x - \frac{1}{20} x^{2}

t^{3} - 12 t^{2} + 36 t

\frac{\partial}{\partial x} (cos (b x + c) e^{x y} x)

What is the derivative of (sqrt(x+1)/(x^2-5)) ?
The derivative of (sqrt(x+1)/(x^2-5)) is (-3x^2-4x-5)/(2(x^2-5)^2sqrt(x+1))
What is the first derivative of (sqrt(x+1)/(x^2-5)) ?
The first derivative of (sqrt(x+1)/(x^2-5)) is (-3x^2-4x-5)/(2(x^2-5)^2sqrt(x+1))