What is the derivative of 3cos(x/2) ?

The derivative of 3cos(x/2) is -3/2 sin(x/2)

What is the first derivative of 3cos(x/2) ?

The first derivative of 3cos(x/2) is -3/2 sin(x/2)

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\frac{d}{d x} (3 cos (\frac{x}{2}))

- \frac{3}{2} sin (\frac{x}{2})

Solution steps

\frac{d}{d x} (3 cos (\frac{x}{2}))

Take the constant out:

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

= 3 \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}

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

Simplify

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

= - \frac{3}{2} sin (\frac{x}{2})

\frac{d y}{d x}, y = - \frac{x}{y}

\int e^{\frac{- x ^{2}}{2}} d x

\frac{d}{d t} (\frac{2 t}{1 + 4 t ^{2}})

\int_{0}^{1} π (2 x^{2})^{2} d x

y^{^{''}} + 4 y = 2 sec (2 t)

What is the derivative of 3cos(x/2) ?
The derivative of 3cos(x/2) is -3/2 sin(x/2)
What is the first derivative of 3cos(x/2) ?
The first derivative of 3cos(x/2) is -3/2 sin(x/2)