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NDA2020MathematicsDifferentiationActual

If x^m y^n=a^ m+n , then what is d y d x equal to?

Options

  1. Am y n x
  2. B- m y n x
  3. Cm x n y
  4. D- n y m x

Correct answer

B. - m y n x

Step-by-step solution

x^m y^n=a^ m+n x^m a^m = a^n y^n (i) Differentiating equation (i) w.r.t. x , we get m x^ (m-1) a^m = a^n (-n) y^ n+1 d y d x d y d x = m y^ (n+1) (x)^ (m-1) -n a^m a^n =- m y n x ( x^m y^n a^ m+n )=- m y n x (1)=- m y n x

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