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Popular >

derivative of arctan(sin(2x))

Solution

\frac{d}{d x} (arctan (sin (2 x)))

Solution

\frac{2 cos ( 2 x )}{sin ^{2} ( 2 x ) + 1}

Solution steps

\frac{d}{d x} (arctan (sin (2 x)))

Apply the chain rule:

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

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

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

= \frac{1}{( sin ( 2 x ) ) ^{2} + 1} cos (2 x) \cdot 2

Simplify

\frac{1}{sin ^{2} ( 2 x ) + 1} cos (2 x) \cdot 2 : \frac{2 cos ( 2 x )}{sin ^{2} ( 2 x ) + 1}

= \frac{2 cos ( 2 x )}{sin ^{2} ( 2 x ) + 1}

Popular Examples

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f (t) = e^{2 (t - 2)}

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d/(dt)(t^3-5t^2+9t)

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Frequently Asked Questions (FAQ)

What is the derivative of arctan(sin(2x)) ?
The derivative of arctan(sin(2x)) is (2cos(2x))/(sin^2(2x)+1)
What is the first derivative of arctan(sin(2x)) ?
The first derivative of arctan(sin(2x)) is (2cos(2x))/(sin^2(2x)+1)