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Popular >

derivative of ln|sin(x|)

Solution

\frac{d}{d x} (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 70pit+35cos((-2pit-pi)/2)derivative of

70 π t + 35 cos (\frac{- 2 π t - π}{2})

integral from 0 to 8 of sin(sqrt(x))

\int_{0}^{8} sin (x) d x

integral of sin(3x)cos(7x)

\int sin (3 x) cos (7 x) d x

x^2y^{''}+3xy^'-24y=0,y(1)=3,y^'(1)=-3

x^{2} y^{^{''}} + 3 x y^{^{'}} - 24 y = 0, y (1) = 3, y^{^{'}} (1) = - 3

(d^2)/(dx^2)(1/x+1/y+xy)

\frac{d ^{2}}{d x ^{2}} (\frac{1}{x} + \frac{1}{y} + x y)

Frequently Asked Questions (FAQ)

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