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Popular >

derivative of sec(x-pi/4)

Solution

\frac{d}{d x} (sec (x - \frac{π}{4}))

Solution

- cot (\frac{π}{4} + x) csc (\frac{π}{4} + x)

Solution steps

\frac{d}{d x} (sec (x - \frac{π}{4}))

Simplify

sec (x - \frac{π}{4}) : csc (\frac{π}{4} + x)

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

Apply the chain rule:

- cot (\frac{π}{4} + x) csc (\frac{π}{4} + x) \frac{d}{d x} (\frac{π}{4} + x)

= - cot (\frac{π}{4} + x) csc (\frac{π}{4} + x) \frac{d}{d x} (\frac{π}{4} + x)

\frac{d}{d x} (\frac{π}{4} + x) = 1

= - cot (\frac{π}{4} + x) csc (\frac{π}{4} + x) \cdot 1

Simplify

= - cot (\frac{π}{4} + x) csc (\frac{π}{4} + x)

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Frequently Asked Questions (FAQ)

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