What is the derivative of cos((npix/2)) ?

The derivative of cos((npix/2)) is -(pinsin((pinx)/2))/(2)

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

The first derivative of cos((npix/2)) is -(pinsin((pinx)/2))/(2)

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\frac{d}{d x} (cos (\frac{nπ x}{2}))

- \frac{πn sin ( \frac{πn x}{2} )}{2}

Solution steps

\frac{d}{d x} (cos (\frac{nπ x}{2}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{nπ x}{2}) = \frac{πn}{2}

= - sin (\frac{nπ x}{2}) \frac{πn}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\int_{0}^{1} x \cdot 2 x d x

6^{2^{x^{2}}}

\int_{0}^{1} \frac{2 x}{( x ^{2} + 1 ) ^{3}} d x

\int (\frac{2}{1 + 2 x}) d x

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

What is the derivative of cos((npix/2)) ?
The derivative of cos((npix/2)) is -(pinsin((pinx)/2))/(2)
What is the first derivative of cos((npix/2)) ?
The first derivative of cos((npix/2)) is -(pinsin((pinx)/2))/(2)