Step by step solution to "Derivatives Find and simplify the derivative of the..."

Clifland

Answered question

2021-10-05

Derivatives Find and simplify the derivative of the following functions

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

Answer & Explanation

Nichole Watt

Skilled2021-10-06Added 100 answers

Step 1
We are aware of this due to the quotient rule of differentiation.
${(\frac{f (x)}{g (x)})}^{'} = \frac{g (x) \cdot f^{'} (x) - f (x) \cdot g^{'} (x)}{{(g (x))}^{2}}$
We have,
$f (x) = \frac{x^{3} - 4 x^{2} + x}{x - 2}$ ...(1)
Step 2
Equation (1)'s two sides are differentiated with respect to x using the quotient rule of derivatives, and the resulting value is as follows:
$f^{'} (x) = \frac{(x - 2) \cdot \frac{d}{d x} (x^{3} - 4 x^{2} + x) - (x^{3} - 4 x^{2} + x) \cdot \frac{d}{d x} (x - 2)}{{(x - 2)}^{2}}$
$f^{'} (x) = \frac{(x - 2) \cdot (3 x^{2} - 8 x + 1) - (x^{3} - 4 x^{2} + x) \cdot (1)}{{(x - 2)}^{2}}$
$f^{'} (x) = \frac{2 x^{3} - 10 x^{2} + 16 x - 2}{x^{2} - 4 x + 4}$
Thus, derived from $f (x) = \frac{x^{3} - 4 x^{2} + x}{x - 2} i s f^{'} (x) = \frac{2 x^{3} - 10 x^{2} + 16 x - 2}{x^{2} - 4 x + 4}$ .

Jeffrey Jordon

Expert2022-08-15Added 2605 answers

Answer is given below (on video)

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