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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Graph

Popular Examples

derivative of ((x^2+1)/(x^2-1))

\frac{d}{d x} (\frac{( x ^{2} + 1 )}{x ^{2} - 1})

integral of (pi-x)cos(pix)

\int (π - x) cos (π x) d x

limit as x approaches 1 of (x-1)/(x^3-1)

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

y^{''}-4y^'-12y=0

y^{^{''}} - 4 y^{^{'}} - 12 y = 0

derivative of 2y derivative of

2 y

Frequently Asked Questions (FAQ)

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