What is the derivative of e^{-4x}cos^4(3x) ?

The derivative of e^{-4x}cos^4(3x) is -4e^{-4x}cos^4(3x)-12e^{-4x}cos^3(3x)sin(3x)

What is the first derivative of e^{-4x}cos^4(3x) ?

The first derivative of e^{-4x}cos^4(3x) is -4e^{-4x}cos^4(3x)-12e^{-4x}cos^3(3x)sin(3x)

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\frac{d}{d x} (e^{- 4 x} cos^{4} (3 x))

- 4 e^{- 4 x} cos^{4} (3 x) - 12 e^{- 4 x} cos^{3} (3 x) sin (3 x)

Solution steps

\frac{d}{d x} (e^{- 4 x} cos^{4} (3 x))

Apply the Product Rule:

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

f = e^{- 4 x}, g = cos^{4} (3 x)

= \frac{d}{d x} (e^{- 4 x}) cos^{4} (3 x) + \frac{d}{d x} (cos^{4} (3 x)) e^{- 4 x}

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

\frac{d}{d x} (cos^{4} (3 x)) = - 12 cos^{3} (3 x) sin (3 x)

= (- 4 e^{- 4 x}) cos^{4} (3 x) + (- 12 cos^{3} (3 x) sin (3 x)) e^{- 4 x}

Simplify

= - 4 e^{- 4 x} cos^{4} (3 x) - 12 e^{- 4 x} cos^{3} (3 x) sin (3 x)

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\frac{\partial}{\partial y} (y ln (x^{2} + y^{3} + 5))

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What is the derivative of e^{-4x}cos^4(3x) ?
The derivative of e^{-4x}cos^4(3x) is -4e^{-4x}cos^4(3x)-12e^{-4x}cos^3(3x)sin(3x)
What is the first derivative of e^{-4x}cos^4(3x) ?
The first derivative of e^{-4x}cos^4(3x) is -4e^{-4x}cos^4(3x)-12e^{-4x}cos^3(3x)sin(3x)