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Popular >

derivative of (x-4^3e^{-4x})

Solution

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

Solution

3 e^{- 4 x} (x - 4)^{2} - 4 e^{- 4 x} (x - 4)^{3}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((x - 4)^{3}) = 3 (x - 4)^{2}

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

= 3 (x - 4)^{2} e^{- 4 x} + (- 4 e^{- 4 x}) (x - 4)^{3}

Simplify

= 3 e^{- 4 x} (x - 4)^{2} - 4 e^{- 4 x} (x - 4)^{3}

Graph

Popular Examples

(dy)/(dx)=e^{3x+5y}

\frac{d y}{d x} = e^{3 x + 5 y}

integral of 4tan^3(x)sec^2(x)

\int 4 tan^{3} (x) sec^{2} (x) d x

derivative of (x^2+1arctan(x))

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

integral of 1/(x^2)-4/(x^3)

\int \frac{1}{x ^{2}} - \frac{4}{x ^{3}} d x

limit as x approaches 0-of 1/(x^3)

x \to 0 - lim (\frac{1}{x ^{3}})

Frequently Asked Questions (FAQ)

What is the derivative of (x-4^3e^{-4x}) ?
The derivative of (x-4^3e^{-4x}) is 3e^{-4x}(x-4)^2-4e^{-4x}(x-4)^3
What is the first derivative of (x-4^3e^{-4x}) ?
The first derivative of (x-4^3e^{-4x}) is 3e^{-4x}(x-4)^2-4e^{-4x}(x-4)^3