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Popular >

derivative of e^{4x}cos(3x)

Solution

\frac{d}{d x} (e^{4 x} cos (3 x))

Solution

4 e^{4 x} cos (3 x) - 3 e^{4 x} sin (3 x)

Solution steps

\frac{d}{d x} (e^{4 x} cos (3 x))

Apply the Product Rule:

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

f = e^{4 x}, g = cos (3 x)

= \frac{d}{d x} (e^{4 x}) cos (3 x) + \frac{d}{d x} (cos (3 x)) e^{4 x}

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= e^{4 x} \cdot 4 cos (3 x) + (- sin (3 x) \cdot 3) e^{4 x}

Simplify

= 4 e^{4 x} cos (3 x) - 3 e^{4 x} sin (3 x)

Popular Examples

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implicit (dy)/(dx),x^2+y^2=25 implicit derivative

\frac{d y}{d x}, x^{2} + y^{2} = 25

Frequently Asked Questions (FAQ)

What is the derivative of e^{4x}cos(3x) ?
The derivative of e^{4x}cos(3x) is 4e^{4x}cos(3x)-3e^{4x}sin(3x)
What is the first derivative of e^{4x}cos(3x) ?
The first derivative of e^{4x}cos(3x) is 4e^{4x}cos(3x)-3e^{4x}sin(3x)