What is the derivative of y=6+4sqrt(x)csc(x) ?

The derivative of y=6+4sqrt(x)csc(x) is 4(-sqrt(x)cot(x)csc(x)+(csc(x))/(2sqrt(x)))

What is the first derivative of y=6+4sqrt(x)csc(x) ?

The first derivative of y=6+4sqrt(x)csc(x) is 4(-sqrt(x)cot(x)csc(x)+(csc(x))/(2sqrt(x)))

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derivative of

y = 6 + 4 x csc (x)

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

Solution steps

\frac{d}{d x} (6 + 4 x csc (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (6) + \frac{d}{d x} (4 x csc (x))

\frac{d}{d x} (6) = 0

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

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

Simplify

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

What is the derivative of y=6+4sqrt(x)csc(x) ?
The derivative of y=6+4sqrt(x)csc(x) is 4(-sqrt(x)cot(x)csc(x)+(csc(x))/(2sqrt(x)))
What is the first derivative of y=6+4sqrt(x)csc(x) ?
The first derivative of y=6+4sqrt(x)csc(x) is 4(-sqrt(x)cot(x)csc(x)+(csc(x))/(2sqrt(x)))