What is the derivative of-e^xcos(x) ?

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

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

The first derivative of-e^xcos(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))

Take the constant out:

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

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

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

f (x) = 2 7 x + 1, at x = 9

1.5 e^{2 x}

f (x) = x \cdot sin (x)

g (t) = 6 t

\frac{d}{d x} (\frac{2}{x ^{3}} + \frac{5}{x ^{2}})

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