Isaiah Alsup

2021-11-22

evaluate y

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,

${y}^{\prime}=\frac{d}{dx}\left(\frac{x-4}{{x}^{2}}\right)$

$=\frac{{x}^{2}\frac{d}{dx}(x-4)-(x-4)\frac{d}{dx}{x}^{2}}{{\left({x}^{2}\right)}^{2}}$

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

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

Further solving it,

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

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

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

$y}^{\prime}=\frac{8-x}{{x}^{3}$

Consider the function,

Step 2

Differentiate the given function with respect to “x” then,

Apply quotient rules of derivatives,

Further solving it,