What is the derivative of (e^x(cos(x))) ?

The derivative of (e^x(cos(x))) is e^xcos(x)-e^xsin(x)

What is the first derivative of (e^x(cos(x))) ?

The first derivative of (e^x(cos(x))) is e^xcos(x)-e^xsin(x)

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

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

Solution steps

\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)

= \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)

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

Simplify

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

(6.1) (1.1)

(2 x + y + 1) (\frac{d y}{d x}) = 1

f (x) = \frac{32}{- 4}

\int_{3}^{4} 3 x cos (x^{2}) d x

\int (3 x + 1)^{3} d x

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