What is the derivative of f(x)=(2x+3)/(x^2+3x+15) ?

The derivative of f(x)=(2x+3)/(x^2+3x+15) is (-2x^2-6x+21)/((x^2+3x+15)^2)

What is the first derivative of f(x)=(2x+3)/(x^2+3x+15) ?

The first derivative of f(x)=(2x+3)/(x^2+3x+15) is (-2x^2-6x+21)/((x^2+3x+15)^2)

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derivative of

f (x) = \frac{2 x + 3}{x ^{2} + 3 x + 15}

\frac{- 2 x ^{2} - 6 x + 21}{( x ^{2} + 3 x + 15 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x + 3}{x ^{2} + 3 x + 15})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x + 3 ) ( x ^{2} + 3 x + 15 ) - \frac{d}{d x} ( x ^{2} + 3 x + 15 ) ( 2 x + 3 )}{( x ^{2} + 3 x + 15 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 3 x + 15) = 2 x + 3

= \frac{2 ( x ^{2} + 3 x + 15 ) - ( 2 x + 3 ) ( 2 x + 3 )}{( x ^{2} + 3 x + 15 ) ^{2}}

Simplify

\frac{2 ( x ^{2} + 3 x + 15 ) - ( 2 x + 3 ) ( 2 x + 3 )}{( x ^{2} + 3 x + 15 ) ^{2}} : \frac{- 2 x ^{2} - 6 x + 21}{( x ^{2} + 3 x + 15 ) ^{2}}

= \frac{- 2 x ^{2} - 6 x + 21}{( x ^{2} + 3 x + 15 ) ^{2}}

\int_{0}^{2} \frac{1}{4 - 2 x} d x

\int_{1}^{5} (2 + 3 x - x^{2}) d x

\frac{1}{10 x}

\int 2 e^{- t} d t

\int \frac{1}{x ^{2} + 2} d x

What is the derivative of f(x)=(2x+3)/(x^2+3x+15) ?
The derivative of f(x)=(2x+3)/(x^2+3x+15) is (-2x^2-6x+21)/((x^2+3x+15)^2)
What is the first derivative of f(x)=(2x+3)/(x^2+3x+15) ?
The first derivative of f(x)=(2x+3)/(x^2+3x+15) is (-2x^2-6x+21)/((x^2+3x+15)^2)