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

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

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Find the Derivative - d/dx cos(x)^2

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int (sec (θ)) d θ

- \frac{d}{d x} y = csc^{2} (x)

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

- \frac{d}{d x} (sin (2 x))

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

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