What is the derivative of arcsin(sqrt(sin(5x))) ?

The derivative of arcsin(sqrt(sin(5x))) is (5cos(5x))/(2sqrt(sin(5x))\sqrt{1-sin(5x))}

What is the first derivative of arcsin(sqrt(sin(5x))) ?

The first derivative of arcsin(sqrt(sin(5x))) is (5cos(5x))/(2sqrt(sin(5x))\sqrt{1-sin(5x))}

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derivative of

arcsin (sin (5 x))

\frac{5 cos ( 5 x )}{2 sin ( 5 x ) 1 - sin ( 5 x )}

Solution steps

\frac{d}{d x} (arcsin (sin (5 x)))

Apply the chain rule:

\frac{1}{1 - ( sin ( 5 x ) ) ^{2}} \frac{d}{d x} (sin (5 x))

= \frac{1}{1 - ( sin ( 5 x ) ) ^{2}} \frac{d}{d x} (sin (5 x))

\frac{d}{d x} (sin (5 x)) = \frac{5 cos ( 5 x )}{2 sin ( 5 x )}

= \frac{1}{1 - ( sin ( 5 x ) ) ^{2}} \cdot \frac{5 cos ( 5 x )}{2 sin ( 5 x )}

Simplify

\frac{1}{1 - ( sin ( 5 x ) ) ^{2}} \cdot \frac{5 cos ( 5 x )}{2 sin ( 5 x )} : \frac{5 cos ( 5 x )}{2 sin ( 5 x ) 1 - sin ( 5 x )}

= \frac{5 cos ( 5 x )}{2 sin ( 5 x ) 1 - sin ( 5 x )}

(x + 3 x) (x^{\frac{3}{2}} - x)

\frac{\partial}{\partial y} (y + e^{x})

x \to 3 lim (5 - 2 x + x^{2})

\frac{1}{( s ^{2} + 8 s + 15 )}

\frac{\partial}{\partial x} (2 x + 6)

What is the derivative of arcsin(sqrt(sin(5x))) ?
The derivative of arcsin(sqrt(sin(5x))) is (5cos(5x))/(2sqrt(sin(5x))\sqrt{1-sin(5x))}
What is the first derivative of arcsin(sqrt(sin(5x))) ?
The first derivative of arcsin(sqrt(sin(5x))) is (5cos(5x))/(2sqrt(sin(5x))\sqrt{1-sin(5x))}