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Popular >

((1-cos(x))/x)^'

Solution

(\frac{1 - cos ( x )}{x})^{^{'}}

Solution

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

Solution steps

(\frac{1 - cos ( x )}{x})^{'}

Apply the Quotient Rule:

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

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

(1 - cos (x))^{'} = sin (x)

x^{'} = 1

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

Simplify

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

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

Popular Examples

integral of (x-2)/(x^2+x+1)

\int \frac{x - 2}{x ^{2} + x + 1} d x

derivative of-csc^2(x-cos(2x)*2)

\frac{d}{d x} (- csc^{2} (x) - cos (2 x) \cdot 2)

(y^2+1)dx=y(sec^2(x))dy

(y^{2} + 1) d x = y (sec^{2} (x)) d y

derivative of (1-x(1+x^2)^{-1})

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

integral of (9+sqrt(x)+x)/x

\int \frac{9 + x + x}{x} d x

Frequently Asked Questions (FAQ)

What is the ((1-cos(x))/x)^' ?
The ((1-cos(x))/x)^' is (xsin(x)-1+cos(x))/(x^2)
What is the first ((1-cos(x))/x)^' ?
The first ((1-cos(x))/x)^' is (xsin(x)-1+cos(x))/(x^2)