Question

suppose that the radius R and area a = πr^2 of a circle are differentiable functions of t. write an equation that relates dA/dt to dr/dt​

Answer 1

Answer:

d A / dt = 4 π r [ d r / dt ]

Step-by-step explanation:

Since:

Area of circle = A(t) = Area is the function of time "t"

Radius of circle = r(t) = radius is the function of time "t"

W Know that

According to the formula of area of circle

                   A(t) = 2 π r²(t).                    ............(1)

Taking derivative of equation (1) with respect to time "t" on both sides

         d A(t) / dt = d (2 π r²(t)) / dt

because " 2 π " is constant here so

⇒        d A(t) / dt = 2 π [ d ( r²(t) ) / dt ]    

Using power rule of derivatives                  

          d A(t) / dt = 2 π ×2 r [ d ( r(t) ) / dt ]

          d A(t) / dt = 4 π r [ d ( r(t) ) / dt ]               .................(2)

Equations (2)  is the required equation

Answer 2

Answer:

Step-by-step explanation:

ChbilalakbarExpert

Answer:

d A / dt = 4 π r [ d r / dt ]

Step-by-step explanation:

Since:

Area of circle = A(t) = Area is the function of time "t"

Radius of circle = r(t) = radius is the function of time "t"

W Know that

According to the formula of area of circle

                   A(t) = 2 π r²(t).                    ............(1)

Taking derivative of equation (1) with respect to time "t" on both sides

         d A(t) / dt = d (2 π r²(t)) / dt

because " 2 π " is constant here so

⇒        d A(t) / dt = 2 π [ d ( r²(t) ) / dt ]    

Using power rule of derivatives                  

          d A(t) / dt = 2 π ×2 r [ d ( r(t) ) / dt ]

          d A(t) / dt = 4 π r [ d ( r(t) ) / dt ]               .................(2)

Equations (2)  is the required equation

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