What is the derivative of y=3e^xcos(x) ?

The derivative of y=3e^xcos(x) is 3(e^xcos(x)-e^xsin(x))

What is the first derivative of y=3e^xcos(x) ?

The first derivative of y=3e^xcos(x) is 3(e^xcos(x)-e^xsin(x))

derivative of

y = 3 e^{x} cos (x)

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

Solution steps

\frac{d}{d x} (3 e^{x} cos (x))

Take the constant out:

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

= 3 \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)

= 3 (\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)

= 3 (e^{x} cos (x) + (- sin (x)) e^{x})

Simplify

= 3 (e^{x} cos (x) - e^{x} sin (x))

\int (\frac{x}{7} - \frac{3}{4} x^{4}) d x

2 t^{2} y^{^{''}} + 3 t y^{^{'}} - y = 0

\int_{0}^{\infty} e^{- \frac{x}{2}} d x

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

y^{^{'}} = \frac{4 x ^{4} e ^{\frac{y}{x}} + x ^{2} y ^{2}}{x ^{3} y}

What is the derivative of y=3e^xcos(x) ?
The derivative of y=3e^xcos(x) is 3(e^xcos(x)-e^xsin(x))
What is the first derivative of y=3e^xcos(x) ?
The first derivative of y=3e^xcos(x) is 3(e^xcos(x)-e^xsin(x))