What is the derivative of 2csc(pi/4 x+1) ?

The derivative of 2csc(pi/4 x+1) is -pi/2 cot((pix)/4)csc((pix)/4)

What is the first derivative of 2csc(pi/4 x+1) ?

The first derivative of 2csc(pi/4 x+1) is -pi/2 cot((pix)/4)csc((pix)/4)

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\frac{d}{d x} (2 csc (\frac{π}{4} x) + 1)

- \frac{π}{2} cot (\frac{π x}{4}) csc (\frac{π x}{4})

Solution steps

\frac{d}{d x} (2 csc (\frac{π}{4} x) + 1)

Simplify

2 csc (\frac{π}{4} x) + 1 : 2 csc (\frac{π x}{4}) + 1

= \frac{d}{d x} (2 csc (\frac{π x}{4}) + 1)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 csc (\frac{π x}{4})) + \frac{d}{d x} (1)

\frac{d}{d x} (2 csc (\frac{π x}{4})) = - \frac{π}{2} cot (\frac{π x}{4}) csc (\frac{π x}{4})

\frac{d}{d x} (1) = 0

= - \frac{π}{2} cot (\frac{π x}{4}) csc (\frac{π x}{4}) + 0

Simplify

= - \frac{π}{2} cot (\frac{π x}{4}) csc (\frac{π x}{4})

What is the derivative of 2csc(pi/4 x+1) ?
The derivative of 2csc(pi/4 x+1) is -pi/2 cot((pix)/4)csc((pix)/4)
What is the first derivative of 2csc(pi/4 x+1) ?
The first derivative of 2csc(pi/4 x+1) is -pi/2 cot((pix)/4)csc((pix)/4)