What is the derivative of e^{5x}cos(3x) ?

The derivative of e^{5x}cos(3x) is 5e^{5x}cos(3x)-3e^{5x}sin(3x)

What is the first derivative of e^{5x}cos(3x) ?

The first derivative of e^{5x}cos(3x) is 5e^{5x}cos(3x)-3e^{5x}sin(3x)

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\frac{d}{d x} (e^{5 x} cos (3 x))

5 e^{5 x} cos (3 x) - 3 e^{5 x} sin (3 x)

Solution steps

\frac{d}{d x} (e^{5 x} cos (3 x))

Apply the Product Rule:

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

f = e^{5 x}, g = cos (3 x)

= \frac{d}{d x} (e^{5 x}) cos (3 x) + \frac{d}{d x} (cos (3 x)) e^{5 x}

\frac{d}{d x} (e^{5 x}) = e^{5 x} \cdot 5

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= e^{5 x} \cdot 5 cos (3 x) + (- sin (3 x) \cdot 3) e^{5 x}

Simplify

= 5 e^{5 x} cos (3 x) - 3 e^{5 x} sin (3 x)

What is the derivative of e^{5x}cos(3x) ?
The derivative of e^{5x}cos(3x) is 5e^{5x}cos(3x)-3e^{5x}sin(3x)
What is the first derivative of e^{5x}cos(3x) ?
The first derivative of e^{5x}cos(3x) is 5e^{5x}cos(3x)-3e^{5x}sin(3x)