What is the derivative of 1/2 sec(x-1/3 csc(x)) ?

The derivative of 1/2 sec(x-1/3 csc(x)) is 1/2 sec(x)tan(x)+1/3 cot(x)csc(x)

What is the first derivative of 1/2 sec(x-1/3 csc(x)) ?

The first derivative of 1/2 sec(x-1/3 csc(x)) is 1/2 sec(x)tan(x)+1/3 cot(x)csc(x)

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\frac{d}{d x} (\frac{1}{2} sec (x) - \frac{1}{3} csc (x))

\frac{1}{2} sec (x) tan (x) + \frac{1}{3} cot (x) csc (x)

Solution steps

\frac{d}{d x} (\frac{1}{2} sec (x) - \frac{1}{3} csc (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{1}{2} sec (x)) - \frac{d}{d x} (\frac{1}{3} csc (x))

\frac{d}{d x} (\frac{1}{2} sec (x)) = \frac{1}{2} sec (x) tan (x)

\frac{d}{d x} (\frac{1}{3} csc (x)) = - \frac{1}{3} cot (x) csc (x)

= \frac{1}{2} sec (x) tan (x) - (- \frac{1}{3} cot (x) csc (x))

Simplify

= \frac{1}{2} sec (x) tan (x) + \frac{1}{3} cot (x) csc (x)

What is the derivative of 1/2 sec(x-1/3 csc(x)) ?
The derivative of 1/2 sec(x-1/3 csc(x)) is 1/2 sec(x)tan(x)+1/3 cot(x)csc(x)
What is the first derivative of 1/2 sec(x-1/3 csc(x)) ?
The first derivative of 1/2 sec(x-1/3 csc(x)) is 1/2 sec(x)tan(x)+1/3 cot(x)csc(x)