Second derivative Assume a curve is given by the

Chapter 8, Problem 88AE

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QUESTION:

Assume a curve is given by the parametric equations x = g(t) and y = h(t), where g and h are twice differentiable. Use the Chain Rule to show that

\(y''(x)=\frac{x'(t)y''(t)-y'(t)x''(t)}{[x'(t)]^3}\).

Questions & Answers

QUESTION:

Assume a curve is given by the parametric equations x = g(t) and y = h(t), where g and h are twice differentiable. Use the Chain Rule to show that

\(y''(x)=\frac{x'(t)y''(t)-y'(t)x''(t)}{[x'(t)]^3}\).

ANSWER:

Solution 88AE

Step 1:

In this problem we have to prove

Given : Assume a curve is given by the parametric equations x = g(t) and y = h(t), where g and h are twice differentiable.

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