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Popular >

derivative of 4cos(x/2)

Solution

\frac{d}{d x} (4 cos (\frac{x}{2}))

Solution

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

Solution steps

\frac{d}{d x} (4 cos (\frac{x}{2}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (cos (\frac{x}{2}))

Apply the chain rule:

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

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

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

= 4 (- sin (\frac{x}{2}) \frac{1}{2})

Simplify

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

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

Popular Examples

y^{^{''}} - 3 y = 0

limit as x approaches 0+of arctan(2/x)

x \to 0 + lim (arctan (\frac{2}{x}))

y^{''}+2y^'+20y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 2 y^{^{'}} + 20 y = 0, y (0) = 1, y^{^{'}} (0) = 0

tangent of f(x)=x-5cos(x),\at x=0 tangent of

f (x) = x - 5 cos (x), at x = 0

sum from n=0 to infinity of (x-10)^n

n = 0 \sum \infty (x - 10)^{n}

Frequently Asked Questions (FAQ)

What is the derivative of 4cos(x/2) ?
The derivative of 4cos(x/2) is -2sin(x/2)
What is the first derivative of 4cos(x/2) ?
The first derivative of 4cos(x/2) is -2sin(x/2)