What is the derivative of (1-cos(x)/(x^2)) ?

The derivative of (1-cos(x)/(x^2)) is (xsin(x)-2(-cos(x)+1))/(x^3)

What is the first derivative of (1-cos(x)/(x^2)) ?

The first derivative of (1-cos(x)/(x^2)) is (xsin(x)-2(-cos(x)+1))/(x^3)

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

\frac{x sin ( x ) - 2 ( - cos ( x ) + 1 )}{x ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x^{2}) = 2 x

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

Simplify

\frac{sin ( x ) x ^{2} - 2 x ( 1 - cos ( x ) )}{( x ^{2} ) ^{2}} : \frac{x sin ( x ) - 2 ( - cos ( x ) + 1 )}{x ^{3}}

= \frac{x sin ( x ) - 2 ( - cos ( x ) + 1 )}{x ^{3}}

\int sin (2 x) 1 + 2 cos (2 x) d x

x \to 2 lim (2 (3))

\int cos^{4} (5 x + 7) d x

1 - 4 x^{2} \frac{d y}{d x} = x

\int - 3 t d t

What is the derivative of (1-cos(x)/(x^2)) ?
The derivative of (1-cos(x)/(x^2)) is (xsin(x)-2(-cos(x)+1))/(x^3)
What is the first derivative of (1-cos(x)/(x^2)) ?
The first derivative of (1-cos(x)/(x^2)) is (xsin(x)-2(-cos(x)+1))/(x^3)