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Popular >

derivative of 1/(sin(x-sin(x)))

Solution

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

Solution

- cot (x - sin (x)) csc (x - sin (x)) (1 - cos (x))

Solution steps

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

Simplify

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

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

Apply the chain rule:

- cot (x - sin (x)) csc (x - sin (x)) \frac{d}{d x} (x - sin (x))

= - cot (x - sin (x)) csc (x - sin (x)) \frac{d}{d x} (x - sin (x))

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

= - cot (x - sin (x)) csc (x - sin (x)) (1 - cos (x))

Popular Examples

derivative of y=(8x^2+4x+2)/(sqrt(x))derivative of

y = \frac{8 x ^{2} + 4 x + 2}{x}

(\partial)/(\partial x)((4x+y)^3(x-y)^2)

\frac{\partial}{\partial x} ((4 x + y)^{3} (x - y)^{2})

(dy)/(dx)=14x^{-8}

\frac{d y}{d x} = 14 x^{- 8}

derivative of x^3-3x^2-9x+15

\frac{d}{d x} (x^{3} - 3 x^{2} - 9 x + 15)

x^{3} + 3 y - x y^{^{'}} = 0

Frequently Asked Questions (FAQ)

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