Find the differential of y in the function: y=^3√t(t^2+4)?

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1 Answer
Mar 24, 2018

#dy/dx=(7*t^(4/3))/3 + 4/(3*t^(2/3)#

Explanation:

Multiply cube root of t in the brackets, we get
#y=(t^(2+1/3)) + 4*t^(1/3)#

This gives us
#y=t^(7/3) + 4t^(1/3)#

On differentiating, we get
#dy/dx=(7*t^(4/3))/3 + (4*t^(-2/3))/3#

Which gives,
#dy/dx=(7*t^(4/3))/3 + 4/(3*t^(2/3)#