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Popular >

derivative of xe^xcsc(x)

Solution

derivative of

x e^{x} csc (x)

Solution

e^{x} csc (x) + x (e^{x} csc (x) - e^{x} cot (x) csc (x))

Solution steps

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

Apply the Product Rule:

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

f = x, g = e^{x} csc (x)

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

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

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

= 1 \cdot e^{x} csc (x) + (e^{x} csc (x) - e^{x} cot (x) csc (x)) x

Simplify

= e^{x} csc (x) + x (e^{x} csc (x) - e^{x} cot (x) csc (x))

Popular Examples

integral of 6y^2+1/(24y^2)

\int 6 y^{2} + \frac{1}{24 y ^{2}} d y

derivative of-5pisin(10pix)derivative of

- 5 π sin (10 π x)

(\partial)/(\partial y)(4x^3y)

\frac{\partial}{\partial y} (4 x^{3} y)

limit as x approaches 0+of (7e^x)/(x^5)

x \to 0 + lim (\frac{7 e ^{x}}{x ^{5}})

limit as x approaches 0 of (e^0-1)/x

x \to 0 lim (\frac{e ^{0} - 1}{x})

Frequently Asked Questions (FAQ)

What is the derivative of xe^xcsc(x) ?
The derivative of xe^xcsc(x) is e^xcsc(x)+x(e^xcsc(x)-e^xcot(x)csc(x))
What is the first derivative of xe^xcsc(x) ?
The first derivative of xe^xcsc(x) is e^xcsc(x)+x(e^xcsc(x)-e^xcot(x)csc(x))