What is the derivative of sqrt(x)csc(x) ?

The derivative of sqrt(x)csc(x) is (csc(x))/(2sqrt(x))-sqrt(x)cot(x)csc(x)

What is the first derivative of sqrt(x)csc(x) ?

The first derivative of sqrt(x)csc(x) is (csc(x))/(2sqrt(x))-sqrt(x)cot(x)csc(x)

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derivative of

x csc (x)

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = csc (x)

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

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

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

= \frac{1}{2 x} csc (x) + (- cot (x) csc (x)) x

Simplify

\frac{1}{2 x} csc (x) + (- cot (x) csc (x)) x : \frac{csc ( x )}{2 x} - x cot (x) csc (x)

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

What is the derivative of sqrt(x)csc(x) ?
The derivative of sqrt(x)csc(x) is (csc(x))/(2sqrt(x))-sqrt(x)cot(x)csc(x)
What is the first derivative of sqrt(x)csc(x) ?
The first derivative of sqrt(x)csc(x) is (csc(x))/(2sqrt(x))-sqrt(x)cot(x)csc(x)