What is the derivative of xe^{5x}cos(2x) ?

The derivative of xe^{5x}cos(2x) is e^{5x}cos(2x)+x(5e^{5x}cos(2x)-2e^{5x}sin(2x))

What is the first derivative of xe^{5x}cos(2x) ?

The first derivative of xe^{5x}cos(2x) is e^{5x}cos(2x)+x(5e^{5x}cos(2x)-2e^{5x}sin(2x))

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\frac{d}{d x} (x e^{5 x} cos (2 x))

e^{5 x} cos (2 x) + x (5 e^{5 x} cos (2 x) - 2 e^{5 x} sin (2 x))

Solution steps

\frac{d}{d x} (x e^{5 x} cos (2 x))

Apply the Product Rule:

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

f = x, g = e^{5 x} cos (2 x)

= \frac{d x}{d x} e^{5 x} cos (2 x) + \frac{d}{d x} (e^{5 x} cos (2 x)) x

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

\frac{d}{d x} (e^{5 x} cos (2 x)) = 5 e^{5 x} cos (2 x) - 2 e^{5 x} sin (2 x)

= 1 \cdot e^{5 x} cos (2 x) + (5 e^{5 x} cos (2 x) - 2 e^{5 x} sin (2 x)) x

Simplify

= e^{5 x} cos (2 x) + x (5 e^{5 x} cos (2 x) - 2 e^{5 x} sin (2 x))

f (x) = 10

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

\int 3 - x d x

15 t^{4} e^{4 t} + 10

6 t \frac{d y}{d t} + 4 y = t

What is the derivative of xe^{5x}cos(2x) ?
The derivative of xe^{5x}cos(2x) is e^{5x}cos(2x)+x(5e^{5x}cos(2x)-2e^{5x}sin(2x))
What is the first derivative of xe^{5x}cos(2x) ?
The first derivative of xe^{5x}cos(2x) is e^{5x}cos(2x)+x(5e^{5x}cos(2x)-2e^{5x}sin(2x))