What is the derivative of 4e^{4x}cos(5x) ?

The derivative of 4e^{4x}cos(5x) is 4(4e^{4x}cos(5x)-5e^{4x}sin(5x))

What is the first derivative of 4e^{4x}cos(5x) ?

The first derivative of 4e^{4x}cos(5x) is 4(4e^{4x}cos(5x)-5e^{4x}sin(5x))

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derivative of

4 e^{4 x} cos (5 x)

4 (4 e^{4 x} cos (5 x) - 5 e^{4 x} sin (5 x))

Solution steps

\frac{d}{d x} (4 e^{4 x} cos (5 x))

Take the constant out:

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

= 4 \frac{d}{d x} (e^{4 x} cos (5 x))

Apply the Product Rule:

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

f = e^{4 x}, g = cos (5 x)

= 4 (\frac{d}{d x} (e^{4 x}) cos (5 x) + \frac{d}{d x} (cos (5 x)) e^{4 x})

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

\frac{d}{d x} (cos (5 x)) = - sin (5 x) \cdot 5

= 4 (e^{4 x} \cdot 4 cos (5 x) + (- sin (5 x) \cdot 5) e^{4 x})

Simplify

= 4 (4 e^{4 x} cos (5 x) - 5 e^{4 x} sin (5 x))

What is the derivative of 4e^{4x}cos(5x) ?
The derivative of 4e^{4x}cos(5x) is 4(4e^{4x}cos(5x)-5e^{4x}sin(5x))
What is the first derivative of 4e^{4x}cos(5x) ?
The first derivative of 4e^{4x}cos(5x) is 4(4e^{4x}cos(5x)-5e^{4x}sin(5x))