math derivative3

Q.1
g(t) = (e3t + 1)5

g’(t)
= d(e3t + 1)5/dt
= [d(e3t + 1)5/d(e3t + 1)] • [d(e3t + 1)/dt]
= 5(e3t + 1)4(3e3t)
= 15e3t(e3t + 1)4

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Q.2

y=xx
lny = xlnx
d(lny)/dx = d(xlnx)/dx
[d(lny)/dy] • (dy/dx) = x[d(lnx)/dx] + (lnx)dx/dx
(1/y)(dy/dx) = x(1/x) + lny
(1/xx)(dy/dx) = 1 + xlnx
dy/dx = xx(1 + xlnx)
=