What is the derivative of f(x)= x/(x^2+10) ?

The derivative of f(x)= x/(x^2+10) is (-x^2+10)/((x^2+10)^2)

What is the first derivative of f(x)= x/(x^2+10) ?

The first derivative of f(x)= x/(x^2+10) is (-x^2+10)/((x^2+10)^2)

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derivative of

f (x) = \frac{x}{x ^{2} + 10}

\frac{- x ^{2} + 10}{( x ^{2} + 10 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} + 10})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x ^{2} + 10 ) - \frac{d}{d x} ( x ^{2} + 10 ) x}{( x ^{2} + 10 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 10) = 2 x

= \frac{1 \cdot ( x ^{2} + 10 ) - 2 xx}{( x ^{2} + 10 ) ^{2}}

1 \cdot (x^{2} + 10) - 2 xx = - x^{2} + 10

= \frac{- x ^{2} + 10}{( x ^{2} + 10 ) ^{2}}

\int 10 sin (x) d x

x \to 2 + lim (\frac{x}{∣ x ∣})

(- 45) (- 4 - 8)

f (x) = - \frac{3}{e ^{3 x}}, x = 0

\int e^{5 x} sin (7 x) d x

What is the derivative of f(x)= x/(x^2+10) ?
The derivative of f(x)= x/(x^2+10) is (-x^2+10)/((x^2+10)^2)
What is the first derivative of f(x)= x/(x^2+10) ?
The first derivative of f(x)= x/(x^2+10) is (-x^2+10)/((x^2+10)^2)