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Popular >

derivative of ln(1-sin(x))

Solution

\frac{d}{d x} (ln (1 - sin (x)))

Solution

- \frac{cos ( x )}{1 - sin ( x )}

Solution steps

\frac{d}{d x} (ln (1 - sin (x)))

Apply the chain rule:

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

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

\frac{d}{d x} (1 - sin (x)) = - cos (x)

= \frac{1}{1 - sin ( x )} (- cos (x))

Simplify

\frac{1}{1 - sin ( x )} (- cos (x)) : - \frac{cos ( x )}{1 - sin ( x )}

= - \frac{cos ( x )}{1 - sin ( x )}

Popular Examples

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

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

y^{''}+9y=cos(5t)

y^{^{''}} + 9 y = cos (5 t)

tangent of y=2x^2+3x,(-2,2)tangent of

y = 2 x^{2} + 3 x, (- 2, 2)

integral of ((sin(3x)-cos(2x)))/4

\int \frac{( sin ( 3 x ) - cos ( 2 x ) )}{4} d x

limit as x approaches-3 of (x^2-4)/(x-2)

x \to - 3 lim (\frac{x ^{2} - 4}{x - 2})

Frequently Asked Questions (FAQ)

What is the derivative of ln(1-sin(x)) ?
The derivative of ln(1-sin(x)) is -(cos(x))/(1-sin(x))
What is the first derivative of ln(1-sin(x)) ?
The first derivative of ln(1-sin(x)) is -(cos(x))/(1-sin(x))