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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

x^{2} - 4, 0

y = x (5^{- 3 x})

\frac{d}{d x} (\frac{3 e ^{x}}{5 e ^{x} + 4})

\frac{d}{d x} (sin^{n - 1} (x))

f (x) = - \frac{3}{x ^{2} - 4}, (1, 1)

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