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

Sum

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

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