What is the derivative of f(x)=ln(sin(2x)) ?

The derivative of f(x)=ln(sin(2x)) is 2cot(2x)

What is the first derivative of f(x)=ln(sin(2x)) ?

The first derivative of f(x)=ln(sin(2x)) is 2cot(2x)

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derivative of

f (x) = ln (sin (2 x))

2 cot (2 x)

Solution steps

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

Apply the chain rule:

\frac{1}{sin ( 2 x )} \frac{d}{d x} (sin (2 x))

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

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

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

Simplify

\frac{1}{sin ( 2 x )} cos (2 x) \cdot 2 : 2 cot (2 x)

= 2 cot (2 x)

\frac{\partial}{\partial x} (ln (tan (x + y)))

\int_{1}^{- 1} (3 e^{x}) d x

\frac{d}{d x} (x e^{x^{3}})

\frac{1}{( s + 3 ) ^{2} + 4}

x^{2} y^{^{'}} - 2 x^{3} e^{- \frac{1}{x}} = y

What is the derivative of f(x)=ln(sin(2x)) ?
The derivative of f(x)=ln(sin(2x)) is 2cot(2x)
What is the first derivative of f(x)=ln(sin(2x)) ?
The first derivative of f(x)=ln(sin(2x)) is 2cot(2x)