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Popular >

derivative of xe^xcos(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

integral of (5x^2+2x^3)

\int (5 x^{2} + 2 x^{3}) d x

x((dy)/(dx))=xtan(y/x)+y

x (\frac{d y}{d x}) = x tan (\frac{y}{x}) + y

integral of (3x+5)^6

\int (3 x + 5)^{6} d x

(\partial)/(\partial x)(5cos(5x))

\frac{\partial}{\partial x} (5 cos (5 x))

limit as x approaches 0+of x/(|x|)

x \to 0 + lim (\frac{x}{∣ x ∣})

Frequently Asked Questions (FAQ)

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