What is the derivative of x/(1+4x^2) ?

The derivative of x/(1+4x^2) is (1-4x^2)/((1+4x^2)^2)

What is the first derivative of x/(1+4x^2) ?

The first derivative of x/(1+4x^2) is (1-4x^2)/((1+4x^2)^2)

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\frac{d}{d x} (\frac{x}{1 + 4 x ^{2}})

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

Solution steps

\frac{d}{d x} (\frac{x}{1 + 4 x ^{2}})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (1 + 4 x^{2}) = 8 x

= \frac{1 \cdot ( 1 + 4 x ^{2} ) - 8 xx}{( 1 + 4 x ^{2} ) ^{2}}

1 \cdot (1 + 4 x^{2}) - 8 xx = 1 - 4 x^{2}

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

\int \frac{k}{x} d x

\int - \frac{x}{e ^{x}} d x

\int (4 - x)^{2} d x

e^{\frac{- x ^{2}}{2}}

\frac{d}{d x} (\frac{4 x}{( x ^{2} + 1 ) ^{2}})

What is the derivative of x/(1+4x^2) ?
The derivative of x/(1+4x^2) is (1-4x^2)/((1+4x^2)^2)
What is the first derivative of x/(1+4x^2) ?
The first derivative of x/(1+4x^2) is (1-4x^2)/((1+4x^2)^2)