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Popular >

derivative of e^x*cos(2x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

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

Simplify

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

Popular Examples

derivative of tan(xsin(x))

\frac{d}{d x} (tan (x) sin (x))

derivative of 4xe^x derivative of

4 x e^{x}

(\partial)/(\partial y)(4x^2+y^2-800)

\frac{\partial}{\partial y} (4 x^{2} + y^{2} - 800)

tangent of f(x)=x^3-8x^2,\at x=0 tangent of

f (x) = x^{3} - 8 x^{2}, at x = 0

integral of sec^6(x)tan^5(x)

\int sec^{6} (x) tan^{5} (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of e^x*cos(2x) ?
The derivative of e^x*cos(2x) is e^xcos(2x)-2e^xsin(2x)
What is the first derivative of e^x*cos(2x) ?
The first derivative of e^x*cos(2x) is e^xcos(2x)-2e^xsin(2x)