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Popular >

derivative of xe^xsin(x)

Solution

\frac{d}{d x} (x \cdot e^{x} \cdot sin (x))

Solution

e^{x} sin (x) + x (e^{x} sin (x) + e^{x} cos (x))

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 1 \cdot e^{x} sin (x) + (e^{x} sin (x) + cos (x) e^{x}) x

Simplify

= e^{x} sin (x) + x (e^{x} sin (x) + e^{x} cos (x))

Popular Examples

integral from 8 to 10 of y/(y^2-4y-5)

\int_{8}^{10} \frac{y}{y ^{2} - 4 y - 5} d y

derivative of f(x)=(-2x^3+x^2-2x-1)x^3 derivative of

f (x) = (- 2 x^{3} + x^{2} - 2 x - 1) x^{3}

y^{''}+64y=sin(8t)

y^{^{''}} + 64 y = sin (8 t)

limit as x approaches 0 of sqrt(x^2+4)

x \to 0 lim (x^{2} + 4)

derivative of 2/(9x^3)

\frac{d}{d x} (\frac{2}{9 x ^{3}})

Frequently Asked Questions (FAQ)

What is the derivative of x*e^x*sin(x) ?
The derivative of x*e^x*sin(x) is e^xsin(x)+x(e^xsin(x)+e^xcos(x))
What is the first derivative of x*e^x*sin(x) ?
The first derivative of x*e^x*sin(x) is e^xsin(x)+x(e^xsin(x)+e^xcos(x))