What is the derivative of arctan(sin(7x)) ?

The derivative of arctan(sin(7x)) is (7cos(7x))/(sin^2(7x)+1)

What is the first derivative of arctan(sin(7x)) ?

The first derivative of arctan(sin(7x)) is (7cos(7x))/(sin^2(7x)+1)

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\frac{d}{d x} (arctan (sin (7 x)))

\frac{7 cos ( 7 x )}{sin ^{2} ( 7 x ) + 1}

Solution steps

\frac{d}{d x} (arctan (sin (7 x)))

Apply the chain rule:

\frac{1}{( sin ( 7 x ) ) ^{2} + 1} \frac{d}{d x} (sin (7 x))

= \frac{1}{( sin ( 7 x ) ) ^{2} + 1} \frac{d}{d x} (sin (7 x))

\frac{d}{d x} (sin (7 x)) = cos (7 x) \cdot 7

= \frac{1}{( sin ( 7 x ) ) ^{2} + 1} cos (7 x) \cdot 7

Simplify

\frac{1}{sin ^{2} ( 7 x ) + 1} cos (7 x) \cdot 7 : \frac{7 cos ( 7 x )}{sin ^{2} ( 7 x ) + 1}

= \frac{7 cos ( 7 x )}{sin ^{2} ( 7 x ) + 1}

What is the derivative of arctan(sin(7x)) ?
The derivative of arctan(sin(7x)) is (7cos(7x))/(sin^2(7x)+1)
What is the first derivative of arctan(sin(7x)) ?
The first derivative of arctan(sin(7x)) is (7cos(7x))/(sin^2(7x)+1)