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Popular >

derivative of ln(sin^2(x))

Solution

derivative of

ln (sin^{2} (x))

Solution

2 cot (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)) = sin (2 x)

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

Simplify

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

= 2 cot (x)

Popular Examples

(dy)/(dx)=x+2xy

\frac{d y}{d x} = x + 2 x y

derivative of (3x+1^3)

\frac{d}{d x} ((3 x + 1)^{3})

sum from n=2 to infinity of 1/(2n*ln(n))

n = 2 \sum \infty \frac{1}{2 n \cdot ln ( n )}

derivative of x^{-2}(5x^2-4)^3 derivative of

x^{- 2} (5 x^{2} - 4)^{3}

(2x^3+xy^2)+(x^2y+2y^3)(dy)/(dx)=0

(2 x^{3} + x y^{2}) + (x^{2} y + 2 y^{3}) \frac{d y}{d x} = 0

Frequently Asked Questions (FAQ)

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