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

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

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

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

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derivative of

f (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)

\frac{\partial}{\partial z} (\frac{( 7 x + 7 y )}{z})

\frac{d}{d x} (- 9 x)

x \to - 3 lim (\frac{x ^{2} - 1}{3 - x})

\frac{d y}{d x} = \frac{2 x}{1 + x ^{2}}

x \to 0 + lim ((4 x)^{\frac{3}{x}})

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