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Popular Calculus >

derivative of e^{mx}cos(nx)

Solution

\frac{d}{d x} (e^{m x} cos (n x))

Solution

m e^{m x} cos (n x) - n e^{m x} sin (n x)

Solution steps

\frac{d}{d x} (e^{m x} cos (n x))

Apply the Product Rule:

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

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

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

\frac{d}{d x} (e^{m x}) = e^{m x} m

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

= e^{m x} m cos (n x) + (- sin (n x) n) e^{m x}

Simplify

= m e^{m x} cos (n x) - n e^{m x} sin (n x)

Graph

Popular Examples

integral of (u^2)/1

\int \frac{u ^{2}}{1} d u

integral from 0 to infinity of ue^{-u}

\int_{0}^{\infty} u e^{- u} d u

limit as x approaches 0 of ((x+1)^3)/x

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

f (x) = coth (x)

taylor 1-1/(x^2)

t a y l or 1 - \frac{1}{x ^{2}}

Frequently Asked Questions (FAQ)

What is the derivative of e^{mx}cos(nx) ?
The derivative of e^{mx}cos(nx) is me^{mx}cos(nx)-ne^{mx}sin(nx)
What is the first derivative of e^{mx}cos(nx) ?
The first derivative of e^{mx}cos(nx) is me^{mx}cos(nx)-ne^{mx}sin(nx)