Surface area Suppose that the radius rr and surface area S=4πr2S=4πr^{2} of a sphere are differentiable functions of tt. Write an equation that relates dS/dtdS/dt to dr/dtdr/dt.

sagnuhh 2020-12-28 Answered
Surface area Suppose that the radius rr and surface area S=4πr2S=4πr2
of a sphere are differentiable functions of tt. Write an equation that relates dS/dtdS/dt to dr/dtdr/dt.
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Expert Answer

hajavaF
Answered 2020-12-29 Author has 90 answers

dSdt=8pirdrdt Knowing implicit differentiation and the given equation, we can take the derivative with respect to t. Doing this we get dSdt=8πrdrdt. We get this by using implicit differentiation and going left to right throughout the problem.

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