What is the derivative of 3e^{5x}cos(6x) ?

The derivative of 3e^{5x}cos(6x) is 3(5e^{5x}cos(6x)-6e^{5x}sin(6x))

What is the first derivative of 3e^{5x}cos(6x) ?

The first derivative of 3e^{5x}cos(6x) is 3(5e^{5x}cos(6x)-6e^{5x}sin(6x))

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derivative of

3 e^{5 x} cos (6 x)

3 (5 e^{5 x} cos (6 x) - 6 e^{5 x} sin (6 x))

Solution steps

\frac{d}{d x} (3 e^{5 x} cos (6 x))

Take the constant out:

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

= 3 \frac{d}{d x} (e^{5 x} cos (6 x))

Apply the Product Rule:

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

f = e^{5 x}, g = cos (6 x)

= 3 (\frac{d}{d x} (e^{5 x}) cos (6 x) + \frac{d}{d x} (cos (6 x)) e^{5 x})

\frac{d}{d x} (e^{5 x}) = e^{5 x} \cdot 5

\frac{d}{d x} (cos (6 x)) = - sin (6 x) \cdot 6

= 3 (e^{5 x} \cdot 5 cos (6 x) + (- sin (6 x) \cdot 6) e^{5 x})

Simplify

= 3 (5 e^{5 x} cos (6 x) - 6 e^{5 x} sin (6 x))

\int \frac{x ^{4} e ^{x} - 6 x ^{3}}{x ^{4}} d x

\frac{2 s}{s + 10}

y = x^{3} + 2, (2, 2)

\frac{\partial}{\partial x} (x y \cdot ln (x + y))

f (x) = 4 x ln (x) - 7 x

What is the derivative of 3e^{5x}cos(6x) ?
The derivative of 3e^{5x}cos(6x) is 3(5e^{5x}cos(6x)-6e^{5x}sin(6x))
What is the first derivative of 3e^{5x}cos(6x) ?
The first derivative of 3e^{5x}cos(6x) is 3(5e^{5x}cos(6x)-6e^{5x}sin(6x))