Key to "Find the derivative of the function. y=4xe−4x+4ex4"

Alyce Wilkinson

Answered question

2021-05-30

Find the derivative of the function.

y = 4 x e^{- 4 x} + 4 e^{x^{4}}

tabuordy

Skilled2021-05-31Added 90 answers

Step 1
Just use basic formulae of derivatives.
Step 2

y = 4 x e^{- 4 x} + 4 e^{x^{4}}

differentiating with respect to x,

∴ \frac{d y}{d x} = \frac{d}{d x} [4 x e^{- 4 x} + 4 e^{x^{4}}]

= 4 \frac{d}{d x} [x e^{- 4 x}] + 4 \frac{d}{d x} [e^{x^{4}}]

= 4 [x (- 4 e^{- 4 x}) + e^{- 4 x} (1)] + 4 (e^{x^{4}}) \cdot \frac{d}{d x} (x^{4})

= 4 [- 4 x e^{- 4 x} + e^{- 4 x}] + 4 e^{x^{4}} \cdot (4 x^{3})

∴ \frac{d y}{d x} = - 16 x e^{- 4 x} + 4 e^{- 4 x} + 16 x^{3} e^{x^{4}}

Jeffrey Jordon

Expert2021-11-24Added 2605 answers

Answer is given below (on video)

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