How do you find #(dy)/(dx)# given #y^4=100x#?

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Answer 1 · 2017-04-16T02:01:22

Please see the explanation

Implicitly differentiate: #y^4=100x#:

#4y^3dy/dx=100#

Divide both sides by #4y^3#:

#dy/dx= 25y^-3#

If you do not want to leave it like this, then you would have been better off solving for y and then differentiating as follows:

#y = sqrt(10)x^(1/4)#

#dy/dx = sqrt(10)/4x^(-3/4)#