What is the derivative of y=e^{8x}cos(11x) ?

The derivative of y=e^{8x}cos(11x) is 8e^{8x}cos(11x)-11e^{8x}sin(11x)

What is the first derivative of y=e^{8x}cos(11x) ?

The first derivative of y=e^{8x}cos(11x) is 8e^{8x}cos(11x)-11e^{8x}sin(11x)

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derivative of

y = e^{8 x} cos (11 x)

8 e^{8 x} cos (11 x) - 11 e^{8 x} sin (11 x)

Solution steps

\frac{d}{d x} (e^{8 x} cos (11 x))

Apply the Product Rule:

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

f = e^{8 x}, g = cos (11 x)

= \frac{d}{d x} (e^{8 x}) cos (11 x) + \frac{d}{d x} (cos (11 x)) e^{8 x}

\frac{d}{d x} (e^{8 x}) = e^{8 x} \cdot 8

\frac{d}{d x} (cos (11 x)) = - sin (11 x) \cdot 11

= e^{8 x} \cdot 8 cos (11 x) + (- sin (11 x) \cdot 11) e^{8 x}

Simplify

= 8 e^{8 x} cos (11 x) - 11 e^{8 x} sin (11 x)

What is the derivative of y=e^{8x}cos(11x) ?
The derivative of y=e^{8x}cos(11x) is 8e^{8x}cos(11x)-11e^{8x}sin(11x)
What is the first derivative of y=e^{8x}cos(11x) ?
The first derivative of y=e^{8x}cos(11x) is 8e^{8x}cos(11x)-11e^{8x}sin(11x)