What is the derivative of (arctan(2x)^{10}) ?

The derivative of (arctan(2x)^{10}) is (20arctan^9(2x))/(4x^2+1)

What is the first derivative of (arctan(2x)^{10}) ?

The first derivative of (arctan(2x)^{10}) is (20arctan^9(2x))/(4x^2+1)

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\frac{d}{d x} ((arctan (2 x))^{10})

\frac{20 arctan ^{9} ( 2 x )}{4 x ^{2} + 1}

Solution steps

\frac{d}{d x} ((arctan (2 x))^{10})

Apply the chain rule:

10 (arctan (2 x))^{9} \frac{d}{d x} (arctan (2 x))

= 10 (arctan (2 x))^{9} \frac{d}{d x} (arctan (2 x))

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

= 10 (arctan (2 x))^{9} \frac{2}{4 x ^{2} + 1}

Simplify

10 arctan^{9} (2 x) \frac{2}{4 x ^{2} + 1} : \frac{20 arctan ^{9} ( 2 x )}{4 x ^{2} + 1}

= \frac{20 arctan ^{9} ( 2 x )}{4 x ^{2} + 1}

What is the derivative of (arctan(2x)^{10}) ?
The derivative of (arctan(2x)^{10}) is (20arctan^9(2x))/(4x^2+1)
What is the first derivative of (arctan(2x)^{10}) ?
The first derivative of (arctan(2x)^{10}) is (20arctan^9(2x))/(4x^2+1)