What is the derivative of f(x)=(x+3)/(x+5) ?

The derivative of f(x)=(x+3)/(x+5) is 2/((x+5)^2)

What is the first derivative of f(x)=(x+3)/(x+5) ?

The first derivative of f(x)=(x+3)/(x+5) is 2/((x+5)^2)

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derivative of

f (x) = \frac{x + 3}{x + 5}

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

Solution steps

\frac{d}{d x} (\frac{x + 3}{x + 5})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x + 3) = 1

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

= \frac{1 \cdot ( x + 5 ) - 1 \cdot ( x + 3 )}{( x + 5 ) ^{2}}

Simplify

\frac{1 \cdot ( x + 5 ) - 1 \cdot ( x + 3 )}{( x + 5 ) ^{2}} : \frac{2}{( x + 5 ) ^{2}}

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

\frac{\partial}{\partial u} (3 u^{2})

\int_{0}^{\frac{π}{2}} π cos^{2} (x) d x

\int \frac{x + 9}{x ^{2} + 4} d x

x \to \infty lim ((x!)^{2})

x^{2} - 12, 4 x

What is the derivative of f(x)=(x+3)/(x+5) ?
The derivative of f(x)=(x+3)/(x+5) is 2/((x+5)^2)
What is the first derivative of f(x)=(x+3)/(x+5) ?
The first derivative of f(x)=(x+3)/(x+5) is 2/((x+5)^2)