What is the derivative of f(x)=e^{3x}cos(6x) ?

The derivative of f(x)=e^{3x}cos(6x) is 3e^{3x}cos(6x)-6e^{3x}sin(6x)

What is the first derivative of f(x)=e^{3x}cos(6x) ?

The first derivative of f(x)=e^{3x}cos(6x) is 3e^{3x}cos(6x)-6e^{3x}sin(6x)

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derivative of

f (x) = e^{3 x} cos (6 x)

3 e^{3 x} cos (6 x) - 6 e^{3 x} sin (6 x)

Solution steps

\frac{d}{d x} (e^{3 x} cos (6 x))

Apply the Product Rule:

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

f = e^{3 x}, g = cos (6 x)

= \frac{d}{d x} (e^{3 x}) cos (6 x) + \frac{d}{d x} (cos (6 x)) e^{3 x}

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

\frac{d}{d x} (cos (6 x)) = - sin (6 x) \cdot 6

= e^{3 x} \cdot 3 cos (6 x) + (- sin (6 x) \cdot 6) e^{3 x}

Simplify

= 3 e^{3 x} cos (6 x) - 6 e^{3 x} sin (6 x)

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

x^{2} + 7 x - 8

\frac{d}{d x} (π cos (x))

e^{x}, e^{- 3 x}, x = ln (5)

\int \frac{x + 5}{x ^{2} + 9} d x

What is the derivative of f(x)=e^{3x}cos(6x) ?
The derivative of f(x)=e^{3x}cos(6x) is 3e^{3x}cos(6x)-6e^{3x}sin(6x)
What is the first derivative of f(x)=e^{3x}cos(6x) ?
The first derivative of f(x)=e^{3x}cos(6x) is 3e^{3x}cos(6x)-6e^{3x}sin(6x)