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

The derivative of 1/(1+4x^2-arctan(2x)) is -(8x)/((1+4x^2)^2)-2/(4x^2+1)

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

The first derivative of 1/(1+4x^2-arctan(2x)) is -(8x)/((1+4x^2)^2)-2/(4x^2+1)

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

e^{- t} sin^{2} (t)

x y^{^{'''}} - \frac{2}{x} y^{^{'}} = 0

\frac{d}{d x} (sin (p (x)) i x)

cos (8 x)

\frac{s}{( s - 3 ) ^{2}}

What is the derivative of 1/(1+4x^2-arctan(2x)) ?
The derivative of 1/(1+4x^2-arctan(2x)) is -(8x)/((1+4x^2)^2)-2/(4x^2+1)
What is the first derivative of 1/(1+4x^2-arctan(2x)) ?
The first derivative of 1/(1+4x^2-arctan(2x)) is -(8x)/((1+4x^2)^2)-2/(4x^2+1)