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Popular >

derivative of y=ln|sin(x)|

Solution

derivative of

y = ln ∣ sin (x) ∣

Solution

cot (x)

Solution steps

\frac{d}{d x} (ln ∣ sin (x) ∣)

Apply the chain rule:

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

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

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

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

Simplify

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

= cot (x)

Popular Examples

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

\frac{d}{d x} ((x^{2 - x})^{5} (x - 3 x^{2}))

integral of (81)/(x^3-9x^2)

\int \frac{81}{x ^{3} - 9 x ^{2}} d x

tangent of (x^2+1)/(x^2+x+1)tangent of

\frac{x ^{2} + 1}{x ^{2} + x + 1}

derivative of f(x)=sqrt(7+10x)derivative of

f (x) = 7 + 10 x

area y=sqrt(x)+1,y=(x^2)/4 ,x=0,x=1 area

y = x + 1, y = \frac{x ^{2}}{4}, x = 0, x = 1

Frequently Asked Questions (FAQ)

What is the derivative of y=ln|sin(x)| ?
The derivative of y=ln|sin(x)| is cot(x)
What is the first derivative of y=ln|sin(x)| ?
The first derivative of y=ln|sin(x)| is cot(x)