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Popular >

derivative of y=e^{3x}cos(6x)

Solution

derivative of

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

Solution

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)

Popular Examples

taylor 1/(1+x^2),1 taylor

\frac{1}{1 + x ^{2}}, 1

tangent of 4/(5x+1)tangent of

\frac{4}{5 x + 1}

(\partial)/(\partial x)(x/(sqrt(x^2+1)))

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + 1})

(dy)/(dt)= y/(t+1)+4t^2+4t,y(1)=-5

\frac{d y}{d t} = \frac{y}{t + 1} + 4 t^{2} + 4 t, y (1) = - 5

limit as x approaches 0 of 1/x-3

x \to 0 lim (\frac{1}{x} - 3)

Frequently Asked Questions (FAQ)

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