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)

\int \frac{2}{3} x d x

\frac{d}{d x} (14 x)

t^{2} y^{^{'}} + t y = 4, y (1) = 3

x \to 3 lim (2 x^{3} - 4 x^{2} + x - 7)

\frac{\partial}{\partial x} (tan (3 x^{2} + 2 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)