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

The derivative of (sqrt(5+x)-sqrt(5))/x is (-x-10+2sqrt(5)sqrt(x+5))/(2x^2sqrt(x+5))

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

The first derivative of (sqrt(5+x)-sqrt(5))/x is (-x-10+2sqrt(5)sqrt(x+5))/(2x^2sqrt(x+5))

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derivative of

\frac{5 + x - 5}{x}

\frac{- x - 10 + 2 5 x + 5}{2 x ^{2} x + 5}

Solution steps

\frac{d}{d x} (\frac{5 + x - 5}{x})

Apply the Quotient Rule:

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

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

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

\frac{d x}{d x} = 1

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

Simplify

\frac{\frac{1}{2 x + 5} x - 1 \cdot ( 5 + x - 5 )}{x ^{2}} : \frac{- x - 10 + 2 5 x + 5}{2 x ^{2} x + 5}

= \frac{- x - 10 + 2 5 x + 5}{2 x ^{2} x + 5}

d y - (y - 8)^{2} d x = 0

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

x y^{^{'}} + y = - 3 x y^{2}, y (1) = 4

\int 17 sin^{2} (2 x) d x

\int \frac{ln ( x )}{x ^{10}} d x

What is the derivative of (sqrt(5+x)-sqrt(5))/x ?
The derivative of (sqrt(5+x)-sqrt(5))/x is (-x-10+2sqrt(5)sqrt(x+5))/(2x^2sqrt(x+5))
What is the first derivative of (sqrt(5+x)-sqrt(5))/x ?
The first derivative of (sqrt(5+x)-sqrt(5))/x is (-x-10+2sqrt(5)sqrt(x+5))/(2x^2sqrt(x+5))