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How do you find the derivative of #y=root3(5x^3 -3x^2 +6) #?

1 Answer

Oct 15, 2015

#dy/dx=(15x^2-6x)/(3root(3)((5x^3-3x^2+6)^2)#

Explanation:

Using laws of indices and surds we may write this function as

#y=(5x^3-3x^2+6)^(1/3)#

Now we may use the power rule to differentiate it as follows :

#dy/dx=1/3(5x^3-3x^2+6)^(-2/3)*(15x^2-6x)#

#=(15x^2-6x)/(3root(3)((5x^3-3x^2+6)^2)#

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