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AP EAMCET202124 Aug 2021Morning ShiftMathematicsDifferentiationActual

If f^ (x)= 2 x^2-1 and y=f (x^3 ) , then find the value of d y d x at x=1

Options

  1. A-1
  2. B3
  3. C0
  4. D-3

Correct answer

B. 3

Step-by-step solution

aligned f^ (x) & = 2 x^2-1 y & =f (x^3 ) aligned Differentiation w.r.t. x array rlr d y d x & =f^ (x^3 ) 3 x^2 [Using chain rule] . d y d x |_ x=1 & =f^ (1^3 ) 3(1)^2 & & =f^ (1) 3 & = 2(1)^2-1 3 [ f^ (x)= 2 x^2-1 ] & = 2-1 3= 1 3 & =3 array

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