What is the derivative of arcsin(sqrt(sin(17x))) ?

The derivative of arcsin(sqrt(sin(17x))) is (17cos(17x))/(2sqrt(sin(17x))\sqrt{1-sin(17x))}

What is the first derivative of arcsin(sqrt(sin(17x))) ?

The first derivative of arcsin(sqrt(sin(17x))) is (17cos(17x))/(2sqrt(sin(17x))\sqrt{1-sin(17x))}

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\frac{d}{d x} (arcsin (sin (17 x)))

\frac{17 cos ( 17 x )}{2 sin ( 17 x ) 1 - sin ( 17 x )}

Solution steps

\frac{d}{d x} (arcsin (sin (17 x)))

Apply the chain rule:

\frac{1}{1 - ( sin ( 17 x ) ) ^{2}} \frac{d}{d x} (sin (17 x))

= \frac{1}{1 - ( sin ( 17 x ) ) ^{2}} \frac{d}{d x} (sin (17 x))

\frac{d}{d x} (sin (17 x)) = \frac{17 cos ( 17 x )}{2 sin ( 17 x )}

= \frac{1}{1 - ( sin ( 17 x ) ) ^{2}} \cdot \frac{17 cos ( 17 x )}{2 sin ( 17 x )}

Simplify

\frac{1}{1 - ( sin ( 17 x ) ) ^{2}} \cdot \frac{17 cos ( 17 x )}{2 sin ( 17 x )} : \frac{17 cos ( 17 x )}{2 sin ( 17 x ) 1 - sin ( 17 x )}

= \frac{17 cos ( 17 x )}{2 sin ( 17 x ) 1 - sin ( 17 x )}

\int \frac{x}{x + 60} d x

(3 - x) \frac{d y}{d x} = y

\int (\frac{t ^{2} - 8 t + 1}{( 2 t ) ^{4}}) d t

f (x) = - 3 x^{2} + 2, at x = 1

What is the derivative of arcsin(sqrt(sin(17x))) ?
The derivative of arcsin(sqrt(sin(17x))) is (17cos(17x))/(2sqrt(sin(17x))\sqrt{1-sin(17x))}
What is the first derivative of arcsin(sqrt(sin(17x))) ?
The first derivative of arcsin(sqrt(sin(17x))) is (17cos(17x))/(2sqrt(sin(17x))\sqrt{1-sin(17x))}