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Chapter 2: Q 19. (page 222)

Find the derivatives of the functions: $f (x) = 3 x^{2} e^{- 4 x}$

Short Answer

Expert verified

The required answer is $- 12 x^{2} e^{- 4 x} + 6 x e^{- 4 x}$ .

Step by step solution

Step 1. Given information.

The given function is: $f (x) = 3 x^{2} e^{- 4 x}$

Step 2. Find the derivative of the given function.

$f (x) = 3 x^{2} e^{- 4 x} = \frac{d}{d x} (3 x^{2} e^{- 4 x}) = 3 x^{2} \frac{d}{d x} (e^{- 4 x}) + e^{- 4 x} \frac{d}{d x} (3 x^{2}) = 3 x^{2} e^{- 4 x} (- 4) + e^{- 4 x} 6 x = - 12 x^{2} e^{- 4 x} + 6 x e^{- 4 x}$

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Find the derivatives of the functions: f(x)=3x2e-4x

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the derivative of the given function.

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Find the derivatives of the functions: $f (x) = 3 x^{2} e^{- 4 x}$