Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: Rs.

There are no items in this cart.
Continue Shopping
Grade: 12th pass
If y is a function of z and z = ax,  then prove that d^2y/dx^2=a^2(d^2y/dx^2) 
one year ago

Answers : (1)

23514 Points

Let y=f(x) , dy/dx = f'(x) and d²y/dx²= f''(x)


We know dy/dz can also be written as


Now if we differentiate the numerator and denominator

We get dy/dz=(dy/dx)÷a = f'(x)/a

Differentiating the the above equation again

We get ,

d²y/dz² = [ d(f'(x))/dz * a - f'(x)*d(a)/dz ] ÷ a² (APPLYING QUOTIENT RULE)

a²*d²y/dz² = d(f'(x))/dx *a *dx/dz - f'(x) *0 (APPLYING CHAIN RULE)

a²*d²x/dz² = f''(x) *a* (dx / d(ax)). (Z=ax)

a²*d²x/dz² = f''(x) *a*(dx/a * dx) (a is taken outside Being a constant , contsant rule)

Cutting a and dx from numerator and denominator (i assume that a is contsant and is not equal to zero. This information is a must. Otherwise the whole question is itself invalid)

We get our final result as

a²*d²x/dz² = f''(x)

= a² * d²x/dz² = d²y/dx²

Hence we have proved the given question!

one year ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies

Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution

Course Features

  • 51 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!! Click Here for details