## Related questions with answers

Question

Verify the chain rule for the functions and curves. $f(x, y, z)=\sqrt{x^2+y^2+z^2} ; \sigma(t)=(\sin t, \cos t, t)$.

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 7Let the function $f(x,y,z)=\sqrt{x^2+y^2+z^2}$ where $x=\sin t, y=\cos t, z=t$. Applying the chain rule we have that:

$\dfrac{df}{dt}=\dfrac{\partial f}{\partial x}\dfrac{dx}{dt}+\dfrac{\partial f}{\partial y}\dfrac{dy}{dt}+\dfrac{\partial f}{\partial z}\dfrac{dz}{dt}$

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