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

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

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

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

= 5 \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)

= 5 (\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

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

Simplify

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

\frac{s}{( s ^{2} + 4 ) ^{2}}

f (x) = 6 sin (x) + 4 cos (x), at x = 0

\int \frac{( arctan ( x ) ) ^{7}}{1 + x ^{2}} d x

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

f (x) = 5 x^{4} e^{x} + e^{x} x^{5}

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