What is the derivative of (2cot(x)/(csc(x))) ?

The derivative of (2cot(x)/(csc(x))) is -2sin(x)

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

The first derivative of (2cot(x)/(csc(x))) is -2sin(x)

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\frac{d}{d x} (\frac{2 cot ( x )}{csc ( x )})

- 2 sin (x)

Solution steps

\frac{d}{d x} (\frac{2 cot ( x )}{csc ( x )})

Simplify

\frac{2 cot ( x )}{csc ( x )} : 2 cot (x) sin (x)

= \frac{d}{d x} (2 cot (x) sin (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (cot (x) sin (x))

Apply the Product Rule:

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

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

= 2 (\frac{d}{d x} (cot (x)) sin (x) + \frac{d}{d x} (sin (x)) cot (x))

\frac{d}{d x} (cot (x)) = - csc^{2} (x)

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

= 2 ((- csc^{2} (x)) sin (x) + cos (x) cot (x))

Simplify

2 ((- csc^{2} (x)) sin (x) + cos (x) cot (x)) : - 2 sin (x)

= - 2 sin (x)

\frac{d}{d x} (I n (- x^{2} + 6 x))

x \to 1 + lim (\frac{x + 9}{x + 2})

\frac{\partial}{\partial x} (4 y x^{3} - 12 y^{2} x^{2})

s e^{- s}

x \to 0 + lim (x^{\frac{3}{x}})

What is the derivative of (2cot(x)/(csc(x))) ?
The derivative of (2cot(x)/(csc(x))) is -2sin(x)
What is the first derivative of (2cot(x)/(csc(x))) ?
The first derivative of (2cot(x)/(csc(x))) is -2sin(x)