What is the derivative of e^{6x}cos(9x) ?

The derivative of e^{6x}cos(9x) is 6e^{6x}cos(9x)-9e^{6x}sin(9x)

What is the first derivative of e^{6x}cos(9x) ?

The first derivative of e^{6x}cos(9x) is 6e^{6x}cos(9x)-9e^{6x}sin(9x)

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derivative of

e^{6 x} cos (9 x)

6 e^{6 x} cos (9 x) - 9 e^{6 x} sin (9 x)

Solution steps

\frac{d}{d x} (e^{6 x} cos (9 x))

Apply the Product Rule:

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

f = e^{6 x}, g = cos (9 x)

= \frac{d}{d x} (e^{6 x}) cos (9 x) + \frac{d}{d x} (cos (9 x)) e^{6 x}

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

\frac{d}{d x} (cos (9 x)) = - sin (9 x) \cdot 9

= e^{6 x} \cdot 6 cos (9 x) + (- sin (9 x) \cdot 9) e^{6 x}

Simplify

= 6 e^{6 x} cos (9 x) - 9 e^{6 x} sin (9 x)

What is the derivative of e^{6x}cos(9x) ?
The derivative of e^{6x}cos(9x) is 6e^{6x}cos(9x)-9e^{6x}sin(9x)
What is the first derivative of e^{6x}cos(9x) ?
The first derivative of e^{6x}cos(9x) is 6e^{6x}cos(9x)-9e^{6x}sin(9x)