Let A be the area of a circle with radius r. If dr/dt=3, find dA/dt when r=3.

Question

anonymous · Answer

Since A = pi(r^2), taking the derivative of both sides gives you dA/dt = pi (2r)(dr/dt).  You have to use the chain rule  when taking the derivative of r. Now just plug in your values. dr/dt = 3, r = 3, so now you have dA/dt = pi (2(3))(3)=18pi

anonymous · Answer

thanks for the step by step

anonymous · Answer

another problem i had trouble with was
Let y=3x^2+6x+3
Find the differential dy when x=2 and dx =0.1
Find the differential dy when x=2 and dx =0.2

for the derivative of y = 6x+6
$$dy=(6x+6)dx$$
from there on i plugged in 6(2)+6(0.1)
i got 12.6 but online says the answer is wrong

anonymous · Answer

ah, you were close, you did the Calculus part right (the derivative), but you made a small mistake while calculating. it would be dy =(6x+6)dx = (6(2)+6)(0.1) = (18)(0.1) = 1.8

anonymous · Answer

ohhh okay i see so the dx is multiplied separately!!
thanks i was wondering what was wrong