What is the derivative of (x^2/(x^2+16)) ?

The derivative of (x^2/(x^2+16)) is (32x)/((x^2+16)^2)

What is the first derivative of (x^2/(x^2+16)) ?

The first derivative of (x^2/(x^2+16)) is (32x)/((x^2+16)^2)

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\frac{d}{d x} (\frac{x ^{2}}{x ^{2} + 16})

\frac{32 x}{( x ^{2} + 16 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} + 16})

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} + 16 ) - \frac{d}{d x} ( x ^{2} + 16 ) x ^{2}}{( x ^{2} + 16 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 16) = 2 x

= \frac{2 x ( x ^{2} + 16 ) - 2 x x ^{2}}{( x ^{2} + 16 ) ^{2}}

Simplify

\frac{2 x ( x ^{2} + 16 ) - 2 x x ^{2}}{( x ^{2} + 16 ) ^{2}} : \frac{32 x}{( x ^{2} + 16 ) ^{2}}

= \frac{32 x}{( x ^{2} + 16 ) ^{2}}

y^{^{''}} - y = x^{2} - 3 x

f (x) = \frac{1}{4 x}

\frac{d}{d x} (x^{3} e^{3 x})

20 e^{- x}

\frac{d}{d x} (3 e^{- x} \cdot tan (3 x))

What is the derivative of (x^2/(x^2+16)) ?
The derivative of (x^2/(x^2+16)) is (32x)/((x^2+16)^2)
What is the first derivative of (x^2/(x^2+16)) ?
The first derivative of (x^2/(x^2+16)) is (32x)/((x^2+16)^2)