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If f(x) and g(x) are two fuctions with g(x)=x-1/x and fog(x)= x 3 -1/x 3 , then f’(x) is equal to?

If f(x) and g(x) are two fuctions with g(x)=x-1/x and fog(x)=x3-1/x3, then f’(x) is equal to?

Grade:11

1 Answers

Ajay
209 Points
7 years ago
solution below...
Given\quad g(x)\quad =\quad x-1/x\quad and\quad fog(x)\quad =\quad x^{ 3 }-\frac { 1 }{ { x }^{ 3 } } \\ Or\quad f[g(x)]\quad =\quad x^{ 3 }-\frac { 1 }{ { x }^{ 3 } } \\ f[x-1/x]\quad =\quad x^{ 3 }-\frac { 1 }{ { x }^{ 3 } } \quad \quad =\quad { (x-1/x) }^{ 3 }-3(x-1/x)\\ put\quad x-1/x\quad =\quad y\\ f(y)\quad =\quad { y }^{ 3 }-3y\\ put\quad y\quad =\quad x\\ f(x)\quad =\quad x^{ 3 }-3x\\ f^{ ` }(x)\quad =\quad 3{ x }^{ 2 }\quad -3
 

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