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Popular >

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

Solution

derivative of

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

Solution

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)

Popular Examples

derivative of f(x)=5(1-x^2)^9 derivative of

f (x) = 5 (1 - x^{2})^{9}

integral of 1/((5x-3)(3-4x))

\int \frac{1}{( 5 x - 3 ) ( 3 - 4 x )} d x

(\partial)/(\partial x)((14x)/(7x^2+y^2+6))

\frac{\partial}{\partial x} (\frac{14 x}{7 x ^{2} + y ^{2} + 6})

area y=2x,(-3,3)area

y = 2 x, (- 3, 3)

integral from 0 to pi/(32) of cos(8x)

\int_{0}^{\frac{π}{32}} cos (8 x) d x

Frequently Asked Questions (FAQ)

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)