Question

I am doing a related rates problem and I don't know how to do implicit differentiation.
Find ds/dt
s=4000+60x+0.02x^2

Answer 1

s=4000+60x+0.02x^2

d/dt[ s ]=d/dt[ 4000+60x+0.02x^2 ]

ds/dt =d/dt[ 4000+60x+0.02x^2 ]

ds/dt =d/dt[ 4000 ]+d/dt[ 60x ]+d/dt[ 0.02x^2 ]

ds/dt =0 +60*d/dt[ x ]+0.02*d/dt[ x^2 ]

ds/dt =0 +60*dx/dt+0.02*2x*dx/dt

ds/dt = 60*dx/dt+0.04x*dx/dt