What is the derivative of f(x)=(120x^2)/(x^2+4) ?

The derivative of f(x)=(120x^2)/(x^2+4) is (960x)/((x^2+4)^2)

What is the first derivative of f(x)=(120x^2)/(x^2+4) ?

The first derivative of f(x)=(120x^2)/(x^2+4) is (960x)/((x^2+4)^2)

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derivative of

f (x) = \frac{120 x ^{2}}{x ^{2} + 4}

\frac{960 x}{( x ^{2} + 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{120 x ^{2}}{x ^{2} + 4})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 120 \frac{d}{d x} (\frac{x ^{2}}{x ^{2} + 4})

Apply the Quotient Rule:

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

= 120 \cdot \frac{\frac{d}{d x} ( x ^{2} ) ( x ^{2} + 4 ) - \frac{d}{d x} ( x ^{2} + 4 ) x ^{2}}{( x ^{2} + 4 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 4) = 2 x

= 120 \cdot \frac{2 x ( x ^{2} + 4 ) - 2 x x ^{2}}{( x ^{2} + 4 ) ^{2}}

Simplify

120 \cdot \frac{2 x ( x ^{2} + 4 ) - 2 x x ^{2}}{( x ^{2} + 4 ) ^{2}} : \frac{960 x}{( x ^{2} + 4 ) ^{2}}

= \frac{960 x}{( x ^{2} + 4 ) ^{2}}

What is the derivative of f(x)=(120x^2)/(x^2+4) ?
The derivative of f(x)=(120x^2)/(x^2+4) is (960x)/((x^2+4)^2)
What is the first derivative of f(x)=(120x^2)/(x^2+4) ?
The first derivative of f(x)=(120x^2)/(x^2+4) is (960x)/((x^2+4)^2)