If $f (x) = \frac{g (x^{6})}{x^{2}}$ $f(x)=g(x^6)/x^2$ , and if g is a differentiable function, find an expression for $f''(x)$ ?

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Answer 1 · 2018-02-03T23:33:24

$f''(x)=(-4x^5(g'(x^6))+x^2(g''(x^6))-2x(g(x^6))-2(g(x^6)))/x^4$

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$f(x)=(g(x^6))/x^2$

$f'(x)=(x^2(g'(x^6))-(g(x^6))(2x))/x^4$

$f''(x)=(x^4((2x)(g'(x^6))+x^2(g''(x^6)-(g'(x^6))(2x)-(g(x^6))(2))-4x^3(x^2(g'(x^6))-(g(x^6))(2x))))/x^8$

$f''(x)=(2x^5(g'(x^6))+x^6(g''(x^6))-2x^5(g'(x^6))-2x^4(g(x^6))-4x^9(g'(x^6))-2x^5(g(x^6)))/x^8$

$f''(x)=(cancelcolor(red)(2x^5(g'(x^6)))+x^6(g''(x^6))cancelcolor(red)(-2x^5(g'(x^6)))-2x^4(g(x^6))-4x^9(g'(x^6))-2x^5(g(x^6)))/x^8$

$f''(x)=(x^4(-4x^5(g'(x^6))+x^2(g''(x^6))-2x(g(x^6))-2(g(x^6))))/(x^4(x^4)$

$f''(x)=(cancelcolor(red)(x^4)(-4x^5(g'(x^6))+x^2(g''(x^6))-2x(g(x^6))-2(g(x^6))))/(cancelcolor(red)(x^4)(x^4)$

$f''(x)=(-4x^5(g'(x^6))+x^2(g''(x^6))-2x(g(x^6))-2(g(x^6)))/x^4$

If f(x)=g(x^6)/x^2f(x)=g(x6)x2f(x)=g(x^6)/x^2 , and if g is a differentiable function, find an expression for f''(x)f''(x) ?