What is the -derivative of cos(x) ?

The -derivative of cos(x) is -x derivative of cos(x)-xsin(x)-cos(x)+C

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Find the Derivative - d/dx cos(x)

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int - x cos (x) d x = - x sin (x) - cos (x)

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

Simplify

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

Add a constant to the solution

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

\int (\frac{1}{( e ^{x} )}) d x

- \frac{d}{d x} y = sec (x) + tan (x)

x \to \infty lim (\frac{x}{2})

sin (θ)

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

What is the -derivative of cos(x) ?
The -derivative of cos(x) is -x derivative of cos(x)-xsin(x)-cos(x)+C