How do you find #(dy)/(dx)# given #y=x^3/3-1#?

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Answer 1 · 2018-04-02T00:43:56

#dy/dx=x^(2)#

We have:

#y=x^3/3-1# Apply #d/dx# on both sides.

#=>d/dx[y]=d/dx[1/3x^3-1]#

#=>d/dx[y]=d/dx[1/3x^3]-d/dx[1]#

A derivative of a constant is always 0.

#=>dy/dx=1/3*d/dx[x^3]-0#

#d/dx[x^n]=nx^(n-1)# if #n# is a constant.

#=>dy/dx=1/3*3*x^(3-1)-0#

#=>dy/dx=1*x^(2)-0#

#=>dy/dx=x^(2)#