What is the derivative of f(x)= x/(x^2+7x+6) ?

The derivative of f(x)= x/(x^2+7x+6) is (-x^2+6)/((x^2+7x+6)^2)

What is the first derivative of f(x)= x/(x^2+7x+6) ?

The first derivative of f(x)= x/(x^2+7x+6) is (-x^2+6)/((x^2+7x+6)^2)

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derivative of

f (x) = \frac{x}{x ^{2} + 7 x + 6}

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

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} + 7 x + 6})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x ^{2} + 7 x + 6 ) - \frac{d}{d x} ( x ^{2} + 7 x + 6 ) x}{( x ^{2} + 7 x + 6 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{2} + 7 x + 6) = 2 x + 7

= \frac{1 \cdot ( x ^{2} + 7 x + 6 ) - ( 2 x + 7 ) x}{( x ^{2} + 7 x + 6 ) ^{2}}

Simplify

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

= \frac{- x ^{2} + 6}{( x ^{2} + 7 x + 6 ) ^{2}}

3 + t

y = x^{2} + 4

\frac{d y}{d x} = (x - 3) e^{(- 2 y)}

\frac{d}{d x} (\frac{e ^{3 x} sin ( 2 x )}{5 ^{x}})

\int \frac{cot ( x )}{1 - sin ( x )} d x

What is the derivative of f(x)= x/(x^2+7x+6) ?
The derivative of f(x)= x/(x^2+7x+6) is (-x^2+6)/((x^2+7x+6)^2)
What is the first derivative of f(x)= x/(x^2+7x+6) ?
The first derivative of f(x)= x/(x^2+7x+6) is (-x^2+6)/((x^2+7x+6)^2)