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Find dydxify=1+x2+x - Mathematics and Statistics

Sum

Find `dy/dx if y=(1+x)/(2+x)`

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Solution

`y=(1+x)/(2+x)`

Differentiating w.r.t. x, we get

`dy/dx = d/dx ((1+x)/(2+x))`

=`((2 + x)d/dx(1 + x) - (1 + x)d/dx(2 + x))/(2 + x)^2`

=`((2 + x)(0 + 1) - (1 + x)(0 + 1))/(2 + x)^2`

`dy/dx = ((2 + x) - (1 + x))/(2 + x)^2`

=`(2 + x - 1 - x)/(2 + x)^2`

=`1/(2 + x)^2`

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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 9 Differentiation
Miscellaneous Exercise 9 | Q II. (7) | Page 123
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