What is the derivative of (sqrt(x)-7/(sqrt(x)+7)) ?

The derivative of (sqrt(x)-7/(sqrt(x)+7)) is 7/(sqrt(x)(\sqrt{x)+7)^2}

What is the first derivative of (sqrt(x)-7/(sqrt(x)+7)) ?

The first derivative of (sqrt(x)-7/(sqrt(x)+7)) is 7/(sqrt(x)(\sqrt{x)+7)^2}

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\frac{d}{d x} (\frac{x - 7}{x + 7})

\frac{7}{x ( x + 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 7}{x + 7})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 7 ) ( x + 7 ) - \frac{d}{d x} ( x + 7 ) ( x - 7 )}{( x + 7 ) ^{2}}

\frac{d}{d x} (x - 7) = \frac{1}{2 x}

\frac{d}{d x} (x + 7) = \frac{1}{2 x}

= \frac{\frac{1}{2 x} ( x + 7 ) - \frac{1}{2 x} ( x - 7 )}{( x + 7 ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( x + 7 ) - \frac{1}{2 x} ( x - 7 )}{( x + 7 ) ^{2}} : \frac{7}{x ( x + 7 ) ^{2}}

= \frac{7}{x ( x + 7 ) ^{2}}

\int 9 x^{\frac{2}{3}} d x

x \to - \infty lim (3 - 2^{x})

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\int_{0}^{8} \frac{2}{x ^{\frac{2}{3}}} d x

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What is the derivative of (sqrt(x)-7/(sqrt(x)+7)) ?
The derivative of (sqrt(x)-7/(sqrt(x)+7)) is 7/(sqrt(x)(\sqrt{x)+7)^2}
What is the first derivative of (sqrt(x)-7/(sqrt(x)+7)) ?
The first derivative of (sqrt(x)-7/(sqrt(x)+7)) is 7/(sqrt(x)(\sqrt{x)+7)^2}