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Grade 12Differential Calculus

A functions(x) is so defined that for all x,(f(x))^n=f(nx) .if f`(x) denotes derivate of f(x) w.r.t x then f`(x).f(nx)=

Profile image of Mansi
9 Years agoGrade 12
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1 Answer

Profile image of Vikas TU
9 Years ago
We have (f(x))^n=f(nx)
Differentiating w.r.t  x we get
 
n(f(x))n-1 . f’(x) = f’(nx).n
  • (f(x))n-1 . f’(x) = f’(nx)
  • (f(x))n . f’(x) = f’(nx) . f(x)    [Multiplying both sides by f(x)]
  • f(nx) . f’(x) = f’(nx) . f(x)    

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