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Daniaal Sanchez

Answered question

2021-10-15

Derivatives Find and simplify the derivative of the following functions

f (x) = e^{x} (x^{3} - 3 x^{2} + 6 x - 6)

Answer & Explanation

Margot Mill

Skilled2021-10-16Added 106 answers

Step 1
Let y = f(x) and z = f(x)
Then

d \frac{y \cdot z}{d x} = y \cdot [\frac{d z}{d x}] + z \cdot [\frac{d y}{d x}]

Step 2

f (x) = e^{x} (x^{3} - 3 x^{2} + 6 x - 6)

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

f^{'} (x) = e^{x} {(x^{3} - 3 x^{2} + 6 x - 6)}^{'} + {(e^{x})}^{'} (x^{3} - 3 x^{2} + 6 x - 6)

= e^{x} [3 x^{2} - 6 x + 6 + x^{3} - 3 x^{2} + 6 x - 6]

= e^{x} [x^{3}]

= e^{x} \cdot x^{3}

f^{'} (x) = e^{x} \cdot x^{3}

Jeffrey Jordon

Expert2022-08-13Added 2605 answers

Answer is given below (on video)

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