What is the derivative of (sqrt(x)-8/(sqrt(x)+8)) ?

The derivative of (sqrt(x)-8/(sqrt(x)+8)) is 8/(sqrt(x)(\sqrt{x)+8)^2}

What is the first derivative of (sqrt(x)-8/(sqrt(x)+8)) ?

The first derivative of (sqrt(x)-8/(sqrt(x)+8)) is 8/(sqrt(x)(\sqrt{x)+8)^2}

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\frac{d}{d x} (\frac{x - 8}{x + 8})

\frac{8}{x ( x + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 8}{x + 8})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 8 ) ( x + 8 ) - \frac{d}{d x} ( x + 8 ) ( x - 8 )}{( x + 8 ) ^{2}}

\frac{d}{d x} (x - 8) = \frac{1}{2 x}

\frac{d}{d x} (x + 8) = \frac{1}{2 x}

= \frac{\frac{1}{2 x} ( x + 8 ) - \frac{1}{2 x} ( x - 8 )}{( x + 8 ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( x + 8 ) - \frac{1}{2 x} ( x - 8 )}{( x + 8 ) ^{2}} : \frac{8}{x ( x + 8 ) ^{2}}

= \frac{8}{x ( x + 8 ) ^{2}}

x \to 4 lim ((x - 4)^{5} - 5)

x \to 3 lim (- 1)

\frac{d}{d x} (\frac{3}{4} x^{\frac{4}{3}} - \frac{3}{8} x^{\frac{2}{3}} + 5)

f (x) = 2 - x

f (x) = \frac{1}{2 x ^{2}}

What is the derivative of (sqrt(x)-8/(sqrt(x)+8)) ?
The derivative of (sqrt(x)-8/(sqrt(x)+8)) is 8/(sqrt(x)(\sqrt{x)+8)^2}
What is the first derivative of (sqrt(x)-8/(sqrt(x)+8)) ?
The first derivative of (sqrt(x)-8/(sqrt(x)+8)) is 8/(sqrt(x)(\sqrt{x)+8)^2}