What is the derivative of f(x)= x/((x^2+15x+50)) ?

The derivative of f(x)= x/((x^2+15x+50)) is (-x^2+50)/((x^2+15x+50)^2)

What is the first derivative of f(x)= x/((x^2+15x+50)) ?

The first derivative of f(x)= x/((x^2+15x+50)) is (-x^2+50)/((x^2+15x+50)^2)

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derivative of

f (x) = \frac{x}{( x ^{2} + 15 x + 50 )}

\frac{- x ^{2} + 50}{( x ^{2} + 15 x + 50 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} + 15 x + 50})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x ^{2} + 15 x + 50 ) - \frac{d}{d x} ( x ^{2} + 15 x + 50 ) x}{( x ^{2} + 15 x + 50 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 15 x + 50) = 2 x + 15

= \frac{1 \cdot ( x ^{2} + 15 x + 50 ) - ( 2 x + 15 ) x}{( x ^{2} + 15 x + 50 ) ^{2}}

Simplify

\frac{1 \cdot ( x ^{2} + 15 x + 50 ) - ( 2 x + 15 ) x}{( x ^{2} + 15 x + 50 ) ^{2}} : \frac{- x ^{2} + 50}{( x ^{2} + 15 x + 50 ) ^{2}}

= \frac{- x ^{2} + 50}{( x ^{2} + 15 x + 50 ) ^{2}}

1 - x, y = 2, - 1, 1

\frac{d}{d x} (x^{2} 3 - 4 x)

\frac{\partial}{\partial y} (3 x e^{2 x y})

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

\frac{x}{x - 4}

What is the derivative of f(x)= x/((x^2+15x+50)) ?
The derivative of f(x)= x/((x^2+15x+50)) is (-x^2+50)/((x^2+15x+50)^2)
What is the first derivative of f(x)= x/((x^2+15x+50)) ?
The first derivative of f(x)= x/((x^2+15x+50)) is (-x^2+50)/((x^2+15x+50)^2)