Find the values of the derivatives dy/dx at x=3 if y=1-1/x

Step 1 Given: y=1−1x Differentiate with y=1−1x respect to x, dydx=ddx(1−1x) =ddx(1)−ddx(1x) =0−(−1x2) =1x2 Step 2 To find dydxatx=3, dydx∣x=3=1(3)2 =13

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Bobbie Comstock

Answered question

2021-12-08

Find the values of the derivatives
dy/dx at

x = \sqrt{3}

if y=1-1/x

Answer & Explanation

twineg4

Beginner2021-12-09Added 33 answers

Step 1
Given:

y = 1 - \frac{1}{x}

Differentiate with

y = 1 - \frac{1}{x}

respect to x,

\frac{d y}{d x} = \frac{d}{d x} (1 - \frac{1}{x})

= \frac{d}{d x} (1) - \frac{d}{d x} (\frac{1}{x})

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

= \frac{1}{x^{2}}

Step 2
To find

\frac{d y}{d x} a t x = \sqrt{3}

\frac{d y}{d x} ∣_{x = \sqrt{3}} = \frac{1}{{(\sqrt{3})}^{2}}

= \frac{1}{3}

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