Let f(x,y)=x^3y and c(t)=(2t^2,t^3) (b) Use the chain rule for paths to evaluate

ID: 2864118 • Letter: L

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Let f(x,y)=x^3y and c(t)=(2t^2,t^3)

(b) Use the chain rule for paths to evaluate d/df f(c(t)) at t=-1

Let f(x,y) = x^3y and c(t) = (2t^2,t^3) (a) Calculate: Nabla f.c(t)= 12x^2yt+3x^3t^2 (b) Use the Chain Rule for Paths to evaluate d/dt f(c(t)) at t=-1. d/dt f(c(-1))=24 pi Note: You can earn partial credit on this problem. Preview Answers Submit Answers Your score was recorded. You have attempted this problem 9 times. You received a score of 50% for this attempt. Your overall recorded score is 50%. You have unlimited attempts remaining. Let f(x,y)=x^3y and c(t)=(2t^2,t^3) (b) Use the chain rule for paths to evaluate d/df f(c(t)) at t=-1

Explanation / Answer

f(x,y)=x^3y and c(t)=(2t^2,t^3)

f(c(t) =(2t^2)^3 t^3

= 8t^9

d/dt f(c(t)) = 72 t^8

at t=-1

= 72

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Let f(x,y)=x^3y and c(t)=(2t^2,t^3) (b) Use the chain rule for paths to evaluate

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