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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = e^{2 x}, g = cos (x)

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

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

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

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

Simplify

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

Popular Examples

integral of y/((x^2+y^2)^{3/2)}

\int \frac{y}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}} d y

derivative of 5e^{8t+9}derivative of

5 e^{8 t + 9}

derivative of (2x^3+5)/x derivative of

\frac{2 x ^{3} + 5}{x}

derivative of y=sin^5(x)derivative of

y = sin^{5} (x)

integral of (x-2)/(x^2+3x)

\int \frac{x - 2}{x ^{2} + 3 x} d x

Frequently Asked Questions (FAQ)

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