What is the derivative of sin(pi/2 x) ?

The derivative of sin(pi/2 x) is cos((pix)/2) pi/2

What is the first derivative of sin(pi/2 x) ?

The first derivative of sin(pi/2 x) is cos((pix)/2) pi/2

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\frac{d}{d x} (sin (\frac{π}{2} x))

cos (\frac{π x}{2}) \frac{π}{2}

Solution steps

\frac{d}{d x} (sin (\frac{π}{2} x))

Simplify

sin (\frac{π}{2} x) : sin (\frac{π x}{2})

= \frac{d}{d x} (sin (\frac{π x}{2}))

Apply the chain rule:

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

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

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

= cos (\frac{π x}{2}) \frac{π}{2}

What is the derivative of sin(pi/2 x) ?
The derivative of sin(pi/2 x) is cos((pix)/2) pi/2
What is the first derivative of sin(pi/2 x) ?
The first derivative of sin(pi/2 x) is cos((pix)/2) pi/2