If #y = x^3 * x^(1/2)# and #t = 3 - ln(x)#, then dy/dt = ?

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Answer 1 · 2018-04-26T02:08:38

#dy/dt = -7/2e^(21/2-7/2t)#

Given:

#y = x^3 * x^(1/2)" [1]"#

#t = 3 - ln(x)" [2]"#

Solve equation [2] for x:

#ln(x) = 3-t#

#x = e^(3-t)" [2.1]"#

Simplify equation [1]:

#y = x^3*x^(1/2)" [1]"#

#y = x^(7/2)" [1.1]"#

Substitute equation [2.1] into equation [1.1]:

#y = (e^(3-t))^(7/2)#

Simplify:

#y = e^(21/2-7/2t)#

#dy/dt = -7/2e^(21/2-7/2t)#