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  • 26-03-2022
  • Mathematics
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Calculus 3.10 Linearization (a) y=x^2sin2x (b) y=ln sqrt(1+t^2) find the differential of each.

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Аноним Аноним
  • 26-03-2022

Answer:

Below in bold.

Step-by-step explanation:

(a) y=x^2sin2x

Using the Product Rule:

dy/dx = x^2*2cos2x + 2xsin2x

dy/dx = 2x(xcos2x + sin2x).

(b) y=ln sqrt(1+t^2)

     y = ln (1 + t^2)^1/2

Using the chain rule:

dy/dx =  1 / (1 + t^2)^1/2 * 1/2(1 + t^2)^-1/2 * 2t

=  2t/(1 + t^2)^1/2 * 1/ (2(1 + t^2)^1/2

=   2t / 2(1 + t^2)

= t / ( 1 + t^2).

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