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Popular >

derivative of e^{2x}cos(pix)

Solution

\frac{d}{d x} (e^{2 x} cos (π x))

Solution

2 e^{2 x} cos (π x) - π e^{2 x} sin (π x)

Solution steps

\frac{d}{d x} (e^{2 x} cos (π x))

Apply the Product Rule:

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

f = e^{2 x}, g = cos (π x)

= \frac{d}{d x} (e^{2 x}) cos (π x) + \frac{d}{d x} (cos (π x)) e^{2 x}

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

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

= e^{2 x} \cdot 2 cos (π x) + (- sin (π x) π) e^{2 x}

Simplify

= 2 e^{2 x} cos (π x) - π e^{2 x} sin (π x)

Popular Examples

integral of sin(ln(8x))

\int sin (ln (8 x)) d x

derivative of arcsin(x)derivative of

arcsin (x)

(d^2y)/(dx^2)+2/x (dy)/(dx)=3xx

\frac{d ^{2} y}{d x ^{2}} + \frac{2}{x} \frac{d y}{d x} = 3 xx

tangent of f(x)=(x^2+7)(5x+4),\at x=2 tangent of

f (x) = (x^{2} + 7) (5 x + 4), at x = 2

limit as x approaches 0 of 9

x \to 0 lim (9)

Frequently Asked Questions (FAQ)

What is the derivative of e^{2x}cos(pix) ?
The derivative of e^{2x}cos(pix) is 2e^{2x}cos(pix)-pie^{2x}sin(pix)
What is the first derivative of e^{2x}cos(pix) ?
The first derivative of e^{2x}cos(pix) is 2e^{2x}cos(pix)-pie^{2x}sin(pix)