What is the (e^xcos(x))^' ?

The (e^xcos(x))^' is e^xcos(x)-e^xsin(x)

What is the first (e^xcos(x))^' ?

The first (e^xcos(x))^' is e^xcos(x)-e^xsin(x)

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(e^{x} cos (x))^{^{'}}

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

Solution steps

(e^{x} cos (x))^{'}

Apply the Product Rule:

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

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

= (e^{x})^{^{'}} cos (x) + (cos (x))^{^{'}} e^{x}

(e^{x})^{'} = e^{x}

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

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

Simplify

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

\int_{0}^{\frac{π}{2}} cos (5 t) cos (10 t) d t

\int \frac{x ^{3}}{4} d x

x y^{^{'}} - 2 y = \frac{3}{2 x}

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

\int sin^{3} (x) cos^{6} (x) d x

What is the (e^xcos(x))^' ?
The (e^xcos(x))^' is e^xcos(x)-e^xsin(x)
What is the first (e^xcos(x))^' ?
The first (e^xcos(x))^' is e^xcos(x)-e^xsin(x)