What is the derivative of e^{3x}cos(2x) ?

The derivative of e^{3x}cos(2x) is 3e^{3x}cos(2x)-2e^{3x}sin(2x)

What is the first derivative of e^{3x}cos(2x) ?

The first derivative of e^{3x}cos(2x) is 3e^{3x}cos(2x)-2e^{3x}sin(2x)

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derivative of

e^{3 x} cos (2 x)

3 e^{3 x} cos (2 x) - 2 e^{3 x} sin (2 x)

Solution steps

\frac{d}{d x} (e^{3 x} cos (2 x))

Apply the Product Rule:

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

f = e^{3 x}, g = cos (2 x)

= \frac{d}{d x} (e^{3 x}) cos (2 x) + \frac{d}{d x} (cos (2 x)) e^{3 x}

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

= e^{3 x} \cdot 3 cos (2 x) + (- sin (2 x) \cdot 2) e^{3 x}

Simplify

= 3 e^{3 x} cos (2 x) - 2 e^{3 x} sin (2 x)

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

(2.3) (4.9)

(15, - 3), (5, 12)

y = \frac{2}{3} x - 3, (0, - 3)

(22, 22)

What is the derivative of e^{3x}cos(2x) ?
The derivative of e^{3x}cos(2x) is 3e^{3x}cos(2x)-2e^{3x}sin(2x)
What is the first derivative of e^{3x}cos(2x) ?
The first derivative of e^{3x}cos(2x) is 3e^{3x}cos(2x)-2e^{3x}sin(2x)