Home > Calculus > Using Implicit Differentiation to Solve Related Rates Problems

If #y=x^3+2x# and #dx/dt=5#, how do you find #dy/dt# when #x=2# ?

Answer 1

Evelyn Agard

By Implicit Differentiation,

#{dy}/{dt}=70#

By differentiating with respect to #t#,

#{dy}/{dt}=d/{dt}(x^3+2x)=(3x^2+2){dx}/{dt}#

by plugging in #x=2# and #{dx}/{dt}=5#,

#=[3(2)^2+2] (5)=70#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Adam Adkins

To find dy/dt when x=2, first find dx/dt=5 at x=2. Then, substitute x=2 and dx/dt=5 into the equation dy/dt = 3x^2(dx/dt) + 2(dx/dt). So, dy/dt = 3(2^2)(5) + 2(5). Calculate this to get the value of dy/dt.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.