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Popular >

derivative of cos(x-1/2 x)

Solution

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

Solution

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

Solution steps

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

Simplify

cos (x) - \frac{1}{2} x : cos (x) - \frac{x}{2}

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

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

Popular Examples

(\partial)/(\partial x)((x+3y)^2)

\frac{\partial}{\partial x} ((x + 3 y)^{2})

v^2dx+x(x+v)dv=0

v^{2} d x + x (x + v) d v = 0

integral of (x^3+2x+5)/(x^2)

\int \frac{x ^{3} + 2 x + 5}{x ^{2}} d x

integral from-2 to 1 of 2-x-x^2

\int_{- 2}^{1} 2 - x - x^{2} d x

sum from n=0 to infinity of n/((n-2)!)

n = 0 \sum \infty \frac{n}{( n - 2 ) !}

Frequently Asked Questions (FAQ)

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