find dy/dx (3xy)^(1/2)=3x-2y
Can't seem to get the solution. May be making a mistake using the chain rule, but I my steps seem correct to me. Would it be easier to first square both sides to get rid of the fractional exponent, then differentiate implicitly? Any help would be appreciated.
Answer6xy-y(3xy)^(1/2))/x(3xy)^(1/2)+4xy
Hello, math34!
Find
Would it be easier to first square both sides to get rid of the fractional exponent,
then differentiate implicitly? . . . absolutely!
Answer: (6xy-y(3xy)^(1/2))/x(3xy)^(1/2)+4xy . . . this can't be right!
Square: .
We have: .
Then: .
Factor: .
Therefore: . . . . which is Dan's answer.
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It can be done head-on . . .
Differentiate implicitly: .
We have: .
We are told that: .
. . Hence, we have: .
Expand: .
Simplify: .
Factor: .
Therefore: .
I am not happy about the idea of squaring the equation, and here's why:
Say we have:
Square both sides:
Now take the derivative:
Now, this certainly is a differential equation for the original function, but we also have another solution: y = -x. In this case the differential equation has more solutions than what we started with.
Just something to watch out for.
-Dan