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))

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

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))

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))