What is the derivative of arcsin(sqrt(sin(7x))) ?

The derivative of arcsin(sqrt(sin(7x))) is (7cos(7x))/(2sqrt(sin(7x))\sqrt{1-sin(7x))}

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

The first derivative of arcsin(sqrt(sin(7x))) is (7cos(7x))/(2sqrt(sin(7x))\sqrt{1-sin(7x))}

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (sin (7 x)) = \frac{7 cos ( 7 x )}{2 sin ( 7 x )}

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

Simplify

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

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

What is the derivative of arcsin(sqrt(sin(7x))) ?
The derivative of arcsin(sqrt(sin(7x))) is (7cos(7x))/(2sqrt(sin(7x))\sqrt{1-sin(7x))}
What is the first derivative of arcsin(sqrt(sin(7x))) ?
The first derivative of arcsin(sqrt(sin(7x))) is (7cos(7x))/(2sqrt(sin(7x))\sqrt{1-sin(7x))}