What is the derivative of (cos(2x))/(sqrt(sin(2x))) ?

The derivative of (cos(2x))/(sqrt(sin(2x))) is (-2sin^2(2x)-cos^2(2x))/(sin(2x)sqrt(sin(2x)))

What is the first derivative of (cos(2x))/(sqrt(sin(2x))) ?

The first derivative of (cos(2x))/(sqrt(sin(2x))) is (-2sin^2(2x)-cos^2(2x))/(sin(2x)sqrt(sin(2x)))

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derivative of

\frac{cos ( 2 x )}{sin ( 2 x )}

\frac{- 2 sin ^{2} ( 2 x ) - cos ^{2} ( 2 x )}{sin ( 2 x ) sin ( 2 x )}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d}{d x} (sin (2 x)) = \frac{1}{2 sin ( 2 x )} cos (2 x) \cdot 2

= \frac{( - sin ( 2 x ) \cdot 2 ) sin ( 2 x ) - \frac{1}{2 s i n ( 2 x )} cos ( 2 x ) \cdot 2 cos ( 2 x )}{( sin ( 2 x ) ) ^{2}}

Simplify

\frac{( - sin ( 2 x ) \cdot 2 ) sin ( 2 x ) - \frac{1}{2 s i n ( 2 x )} cos ( 2 x ) \cdot 2 cos ( 2 x )}{( sin ( 2 x ) ) ^{2}} : \frac{- 2 sin ^{2} ( 2 x ) - cos ^{2} ( 2 x )}{sin ( 2 x ) sin ( 2 x )}

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

\int (4 x^{5} + 3 x + 8) d x

f^{^{'}} (x) = 8 x^{3} - 6 x^{2} + 10 x - 9, f (1) = 24

1 - x^{2}

y = \frac{x}{7 + x}

x \to 1 lim (7 x + 42)

What is the derivative of (cos(2x))/(sqrt(sin(2x))) ?
The derivative of (cos(2x))/(sqrt(sin(2x))) is (-2sin^2(2x)-cos^2(2x))/(sin(2x)sqrt(sin(2x)))
What is the first derivative of (cos(2x))/(sqrt(sin(2x))) ?
The first derivative of (cos(2x))/(sqrt(sin(2x))) is (-2sin^2(2x)-cos^2(2x))/(sin(2x)sqrt(sin(2x)))