What is the derivative of cos(x-pi/4) ?

The derivative of cos(x-pi/4) is cos(pi/4+x)

What is the first derivative of cos(x-pi/4) ?

The first derivative of cos(x-pi/4) is cos(pi/4+x)

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\frac{d}{d x} (cos (x - \frac{π}{4}))

cos (\frac{π}{4} + x)

Solution steps

\frac{d}{d x} (cos (x - \frac{π}{4}))

Simplify

cos (x - \frac{π}{4}) : sin (\frac{π}{4} + x)

= \frac{d}{d x} (sin (\frac{π}{4} + x))

Apply the chain rule:

cos (\frac{π}{4} + x) \frac{d}{d x} (\frac{π}{4} + x)

= cos (\frac{π}{4} + x) \frac{d}{d x} (\frac{π}{4} + x)

\frac{d}{d x} (\frac{π}{4} + x) = 1

= cos (\frac{π}{4} + x) \cdot 1

Simplify

= cos (\frac{π}{4} + x)

What is the derivative of cos(x-pi/4) ?
The derivative of cos(x-pi/4) is cos(pi/4+x)
What is the first derivative of cos(x-pi/4) ?
The first derivative of cos(x-pi/4) is cos(pi/4+x)