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Second derivative Assume a curve is given by the
Chapter 8, Problem 88AE(choose chapter or problem)
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.