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Popular >

derivative of y=6+4sqrt(x)csc(x)

Solution

derivative of

y = 6 + 4 x csc (x)

Solution

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})

Popular Examples

sum from n=1 to infinity of 3/((4n^2-1))

n = 1 \sum \infty \frac{3}{( 4 n ^{2} - 1 )}

(\partial)/(\partial y)((2x+3y)^{10})

\frac{\partial}{\partial y} ((2 x + 3 y)^{10})

xy^'=y-sqrt(x^2+y^2)

x y^{^{'}} = y - x^{2} + y^{2}

x y^{^{'}} = 2 y

sum from n=0 to infinity of-5

n = 0 \sum \infty - 5

Frequently Asked Questions (FAQ)

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)))