Statistics Solutions

[Step-by-Step] If y=f(u) and u=g(x), where f and g are twice differentiable, show that

Question: If \(y=f(u)\) and \(u=g(x)\), where \(f\) and \(g\) are twice differentiable, show that

\[\frac{{{d}^{2}}y}{d{{x}^{2}}}=\frac{{{d}^{2}}y}{d{{u}^{2}}}{{\left( \frac{du}{dx} \right)}^{2}}+\frac{dy}{du}\frac{{{d}^{2}}u}{d{{x}^{2}}}\]

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