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Popular >

derivative of ae^xcos(x)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

(\partial)/(\partial x)(((3x-3z))/(y+3z))

\frac{\partial}{\partial x} (\frac{( 3 x - 3 z )}{y + 3 z})

integral of 10xe^{3x^2-7}

\int 10 x e^{3 x^{2} - 7} d x

integral of 3cos(x)-2sin(x)

\int 3 cos (x) - 2 sin (x) d x

limit as x approaches pi of cos(5/3 x)

x \to π lim (cos (\frac{5}{3} x))

derivative of (sqrt(x)-8)/(sqrt(x)+8)derivative of

\frac{x - 8}{x + 8}

Frequently Asked Questions (FAQ)

What is the derivative of ae^xcos(x) ?
The derivative of ae^xcos(x) is a(e^xcos(x)-e^xsin(x))
What is the first derivative of ae^xcos(x) ?
The first derivative of ae^xcos(x) is a(e^xcos(x)-e^xsin(x))