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

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

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

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

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derivative of

y = 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)

\int x^{2} x + 1 d x

\frac{d}{d x} (sin (x) + x)

\int \frac{2 x}{1 - 4 x ^{4}} d x

\int \frac{z ^{2}}{z ^{3} + 1} d z

- 9 (5 x^{2} + 4)^{- 6}

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