What is the derivative of (sqrt(x)-7/(sqrt(x)+5)) ?

The derivative of (sqrt(x)-7/(sqrt(x)+5)) is 6/(sqrt(x)(\sqrt{x)+5)^2}

What is the first derivative of (sqrt(x)-7/(sqrt(x)+5)) ?

The first derivative of (sqrt(x)-7/(sqrt(x)+5)) is 6/(sqrt(x)(\sqrt{x)+5)^2}

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\frac{d}{d x} (\frac{x - 7}{x + 5})

\frac{6}{x ( x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 7}{x + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 7 ) ( x + 5 ) - \frac{d}{d x} ( x + 5 ) ( x - 7 )}{( x + 5 ) ^{2}}

\frac{d}{d x} (x - 7) = \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 - 7 )}{( x + 5 ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( x + 5 ) - \frac{1}{2 x} ( x - 7 )}{( x + 5 ) ^{2}} : \frac{6}{x ( x + 5 ) ^{2}}

= \frac{6}{x ( x + 5 ) ^{2}}

\frac{d}{d x} (\frac{0.3 ( 9 ^{x} )}{x ^{3}})

\frac{\partial}{\partial x} (x^{2} yz - x y z^{5})

y^{^{'''}} - y^{^{''}} + 7 y^{^{'}} - 7 y = 0

x \to 0 lim (x^{3} x)

\int_{0}^{5} \frac{x + y}{55} d x

What is the derivative of (sqrt(x)-7/(sqrt(x)+5)) ?
The derivative of (sqrt(x)-7/(sqrt(x)+5)) is 6/(sqrt(x)(\sqrt{x)+5)^2}
What is the first derivative of (sqrt(x)-7/(sqrt(x)+5)) ?
The first derivative of (sqrt(x)-7/(sqrt(x)+5)) is 6/(sqrt(x)(\sqrt{x)+5)^2}