What is the derivative of 25cos((pix)/(50)) ?

The derivative of 25cos((pix)/(50)) is -pi/2 sin((pix)/(50))

What is the first derivative of 25cos((pix)/(50)) ?

The first derivative of 25cos((pix)/(50)) is -pi/2 sin((pix)/(50))

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derivative of

25 cos (\frac{π x}{50})

- \frac{π}{2} sin (\frac{π x}{50})

Solution steps

\frac{d}{d x} (25 cos (\frac{π x}{50}))

Take the constant out:

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

= 25 \frac{d}{d x} (cos (\frac{π x}{50}))

Apply the chain rule:

- sin (\frac{π x}{50}) \frac{d}{d x} (\frac{π x}{50})

= - sin (\frac{π x}{50}) \frac{d}{d x} (\frac{π x}{50})

\frac{d}{d x} (\frac{π x}{50}) = \frac{π}{50}

= 25 (- sin (\frac{π x}{50}) \frac{π}{50})

Simplify

25 (- sin (\frac{π x}{50}) \frac{π}{50}) : - \frac{π}{2} sin (\frac{π x}{50})

= - \frac{π}{2} sin (\frac{π x}{50})

What is the derivative of 25cos((pix)/(50)) ?
The derivative of 25cos((pix)/(50)) is -pi/2 sin((pix)/(50))
What is the first derivative of 25cos((pix)/(50)) ?
The first derivative of 25cos((pix)/(50)) is -pi/2 sin((pix)/(50))