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

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

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

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

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derivative of

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{3 x ^{2} + x + 3}{( x - 1 ) ^{3} ( x ^{2} + 1 )} d x

\int \frac{1}{( y - 1 ) ( y + 1 )} d y

\int \frac{1}{x \cdot ( ln ( x ) )} d x

x \to 1 lim (- x^{2} + 4 x - 8)

\frac{3 t}{t}

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