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

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

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

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

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

arctan (2 x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

= arctan (2 x)

9 x^{\frac{3}{5}} - 2 x^{\frac{6}{7}}, at x = 3

x \to - 4 lim (- (x^{2} + 10 x + 8))

f (x) = \frac{3}{( 2 x ) ^{2}}

f (x) = tan (x), (\frac{3 π}{4}, - 1)

x \to 2 π lim (csc (x))

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