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

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

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

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

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

\frac{5}{x ( x + 5 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

y cos (x y) - tan (x) + x cos (x y) y^{^{'}} = 0

(7, 14), (9, 18)

f (x) = 2 x^{3} - 8 x, (2, 0)

x - sin (x)

\frac{d}{d x} (ln (sin (10 x)))

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