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Popular >

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

Solution

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

Solution

\frac{1 - sin ( x ) + x cos ( x )}{( 1 - sin ( x ) ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

Simplify

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

Popular Examples

inverse oflaplace 1/(s(2s^2+2s+1))inverse laplace

\frac{1}{s ( 2 s ^{2} + 2 s + 1 )}

sum from n=0 to infinity of 3/(n^{5/3)}

n = 0 \sum \infty \frac{3}{n ^{\frac{5}{3}}}

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\frac{( x ^{2} - 4 x )}{x + 1}

integral of 1/(x^4)+4

\int \frac{1}{x ^{4}} + 4 d x

implicit (dy)/(dx),x^3+y^3-9xy=0 implicit derivative

\frac{d y}{d x}, x^{3} + y^{3} - 9 x y = 0

Frequently Asked Questions (FAQ)

What is the derivative of x/(1-sin(x)) ?
The derivative of x/(1-sin(x)) is (1-sin(x)+xcos(x))/((1-sin(x))^2)
What is the first derivative of x/(1-sin(x)) ?
The first derivative of x/(1-sin(x)) is (1-sin(x)+xcos(x))/((1-sin(x))^2)