What is the derivative of x/(sqrt(x^4+4)) ?

The derivative of x/(sqrt(x^4+4)) is (-x^4+4)/((x^4+4)sqrt(x^4+4))

What is the first derivative of x/(sqrt(x^4+4)) ?

The first derivative of x/(sqrt(x^4+4)) is (-x^4+4)/((x^4+4)sqrt(x^4+4))

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

\frac{- x ^{4} + 4}{( x ^{4} + 4 ) x ^{4} + 4}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

= \frac{1 \cdot x ^{4} + 4 - \frac{2 x ^{3}}{x ^{4} + 4} x}{( x ^{4} + 4 ) ^{2}}

Simplify

\frac{1 \cdot x ^{4} + 4 - \frac{2 x ^{3}}{x ^{4} + 4} x}{( x ^{4} + 4 ) ^{2}} : \frac{- x ^{4} + 4}{( x ^{4} + 4 ) x ^{4} + 4}

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

\frac{d}{d x} (\frac{x ^{4}}{5 - x ^{3}})

f (x) = ln (5 + ln (x))

3 t e^{- t}

\int_{2}^{e + 1} \frac{1}{x - 1} d x

\int cos^{3} (4 x) sin (4 x) d x

What is the derivative of x/(sqrt(x^4+4)) ?
The derivative of x/(sqrt(x^4+4)) is (-x^4+4)/((x^4+4)sqrt(x^4+4))
What is the first derivative of x/(sqrt(x^4+4)) ?
The first derivative of x/(sqrt(x^4+4)) is (-x^4+4)/((x^4+4)sqrt(x^4+4))