What is the derivative of (cos(x)/(csc(x))) ?

The derivative of (cos(x)/(csc(x))) is cos(2x)

What is the first derivative of (cos(x)/(csc(x))) ?

The first derivative of (cos(x)/(csc(x))) is cos(2x)

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\frac{d}{d x} (\frac{cos ( x )}{csc ( x )})

cos (2 x)

Solution steps

\frac{d}{d x} (\frac{cos ( x )}{csc ( x )})

Simplify

\frac{cos ( x )}{csc ( x )} : cos (x) sin (x)

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (x), g = sin (x)

= \frac{d}{d x} (cos (x)) sin (x) + \frac{d}{d x} (sin (x)) cos (x)

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

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

= (- sin (x)) sin (x) + cos (x) cos (x)

Simplify

(- sin (x)) sin (x) + cos (x) cos (x) : cos (2 x)

= cos (2 x)

\frac{\partial}{\partial x} (8 x^{2} + y^{2})

\frac{\partial}{\partial x} (e^{4 x yz - 7})

y = 3 ln (x), y = 0, x = 2 e

x^{2} y^{^{'}} + 2 x y = sin (4 x)

\int - 2 x 9 - x^{2} d x

What is the derivative of (cos(x)/(csc(x))) ?
The derivative of (cos(x)/(csc(x))) is cos(2x)
What is the first derivative of (cos(x)/(csc(x))) ?
The first derivative of (cos(x)/(csc(x))) is cos(2x)