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15.2 Section 13.4 Progress Check Question 2

Question 15.2 Section 13.4 Progress Check Question 2

Use the chain rule to find the derivative \(\displaystyle \frac{dh}{dt}\) of \(h(t) = f({\bf c}(t)) \) where \(f(x,y,z)= xe^{yz}\) and \({\bf c}(t)=(e^t,t,\sin t)\).

\(\ \ \displaystyle \frac{dh}{dt}= e^t e^{t \sin t}+ e^t e^{t \sin t}\sin t+t e^t e^{t \sin t}\cos t\)

\(\ \ \displaystyle \frac{dh}{dt}= e^t e^{\cos t}+ t e^t e^{\cos t}\cos t +e^t e^{\cos t}\sin t \)

\(\ \ \displaystyle \frac{dh}{dt}= (e^{t\sin t},e^t e^{t\sin t}\sin t, t e^t e^{t\sin t})\)

\(\ \ \displaystyle \frac{dh}{dt}= e^t e^{\cos t}\)

\(\ \ \displaystyle \frac{dh}{dt}= (e^{t\sin t}+e^t,e^t e^{t\sin t}\sin t+1, t e^t e^{t\sin t}+\cos t)\)

Correct.

Incorrect.

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