Step 1Consider the function,y=x−4x2Step 2Differentiate the given function with respect to “x” then,Apply quotient rules of derivatives,y′=ddx(x−4x2)=x2ddx(x−4)−(x−4)ddxx2(x2)2=x2(1−0)−(x−4)(2x)x4=x2−(2x2−8x)x4Further solving it,=x2−2x2+8xx4=−x2+8xx4=x(−x+8)x4y′=8−xx3

Question: "evaluate y"

Isaiah Alsup

Answered question

2021-11-22

evaluate y

Answer & Explanation

David Tyson

Beginner2021-11-23Added 19 answers

Step 1
Consider the function,

y = \frac{x - 4}{x^{2}}

Step 2
Differentiate the given function with respect to “x” then,
Apply quotient rules of derivatives,

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

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

= \frac{x^{2} (1 - 0) - (x - 4) (2 x)}{x^{4}}

= \frac{x^{2} - (2 x^{2} - 8 x)}{x^{4}}

Further solving it,

= \frac{x^{2} - 2 x^{2} + 8 x}{x^{4}}

= \frac{- x^{2} + 8 x}{x^{4}}

= \frac{x (- x + 8)}{x^{4}}

y^{'} = \frac{8 - x}{x^{3}}

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