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

The derivative of f(x)=(x^2)/(x^2+7) is (14x)/((x^2+7)^2)

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

The first derivative of f(x)=(x^2)/(x^2+7) is (14x)/((x^2+7)^2)

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derivative of

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

\frac{14 x}{( x ^{2} + 7 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 x ( x ^{2} + 7 ) - 2 x x ^{2}}{( x ^{2} + 7 ) ^{2}} : \frac{14 x}{( x ^{2} + 7 ) ^{2}}

= \frac{14 x}{( x ^{2} + 7 ) ^{2}}

\int - \frac{ln ( x )}{2} d x

u^{'} (t)

\frac{\partial}{\partial y} (arctan (x - y))

x \to \infty + lim (0)

\int sec^{2} (2 x + 1) d x

What is the derivative of f(x)=(x^2)/(x^2+7) ?
The derivative of f(x)=(x^2)/(x^2+7) is (14x)/((x^2+7)^2)
What is the first derivative of f(x)=(x^2)/(x^2+7) ?
The first derivative of f(x)=(x^2)/(x^2+7) is (14x)/((x^2+7)^2)