What is the derivative of arcsin(sqrt(sin(11x))) ?

The derivative of arcsin(sqrt(sin(11x))) is (11cos(11x))/(2sqrt(sin(11x))\sqrt{1-sin(11x))}

What is the first derivative of arcsin(sqrt(sin(11x))) ?

The first derivative of arcsin(sqrt(sin(11x))) is (11cos(11x))/(2sqrt(sin(11x))\sqrt{1-sin(11x))}

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\frac{d}{d x} (arcsin (sin (11 x)))

\frac{11 cos ( 11 x )}{2 sin ( 11 x ) 1 - sin ( 11 x )}

Solution steps

\frac{d}{d x} (arcsin (sin (11 x)))

Apply the chain rule:

\frac{1}{1 - ( sin ( 11 x ) ) ^{2}} \frac{d}{d x} (sin (11 x))

= \frac{1}{1 - ( sin ( 11 x ) ) ^{2}} \frac{d}{d x} (sin (11 x))

\frac{d}{d x} (sin (11 x)) = \frac{11 cos ( 11 x )}{2 sin ( 11 x )}

= \frac{1}{1 - ( sin ( 11 x ) ) ^{2}} \cdot \frac{11 cos ( 11 x )}{2 sin ( 11 x )}

Simplify

\frac{1}{1 - ( sin ( 11 x ) ) ^{2}} \cdot \frac{11 cos ( 11 x )}{2 sin ( 11 x )} : \frac{11 cos ( 11 x )}{2 sin ( 11 x ) 1 - sin ( 11 x )}

= \frac{11 cos ( 11 x )}{2 sin ( 11 x ) 1 - sin ( 11 x )}

\int \frac{1}{t ^{2} - 2 t + 10} d t

\int cos^{7} (2 x) d x

\frac{\partial}{\partial x} (\frac{2 x}{9 - tan ( x )})

\int \frac{x ^{11}}{2 x ^{6} + 2} d x

y^{^{''}} + y^{^{'}} - 6 y = 2 x

What is the derivative of arcsin(sqrt(sin(11x))) ?
The derivative of arcsin(sqrt(sin(11x))) is (11cos(11x))/(2sqrt(sin(11x))\sqrt{1-sin(11x))}
What is the first derivative of arcsin(sqrt(sin(11x))) ?
The first derivative of arcsin(sqrt(sin(11x))) is (11cos(11x))/(2sqrt(sin(11x))\sqrt{1-sin(11x))}