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Popular >

derivative of x/(csc(x))

Solution

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

Solution

sin (x) + x cos (x)

Solution steps

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

Simplify

\frac{x}{csc ( x )} : x sin (x)

= \frac{d}{d x} (x sin (x))

Apply the Product Rule:

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

f = x, g = sin (x)

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

\frac{d x}{d x} = 1

\frac{d}{d x} (sin (x)) = cos (x)

= 1 \cdot sin (x) + cos (x) x

Simplify

= sin (x) + x cos (x)

Popular Examples

f^{^{'}} (x) = \frac{e ^{x}}{x}

(\partial)/(\partial y)(3ze^{xy})

\frac{\partial}{\partial y} (3 z e^{x y})

integral of (2x+32)/(x^2+8x+7)

\int \frac{2 x + 32}{x ^{2} + 8 x + 7} d x

derivative of y= 1/2 x^3 derivative of

y = \frac{1}{2} x^{3}

derivative of 1/((x+7^2))

\frac{d}{d x} (\frac{1}{( x + 7 ) ^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of x/(csc(x)) ?
The derivative of x/(csc(x)) is sin(x)+xcos(x)
What is the first derivative of x/(csc(x)) ?
The first derivative of x/(csc(x)) is sin(x)+xcos(x)