[tex]\frac{d}{dt} r(g(t))=<4e^{4t+4} ,16e^{16t+4} ,0>[/tex]
Given: [tex]r(t)=<e^{t} ,e^{4t} ,-4>[/tex] and [tex]g(t)=4t+4[/tex]
To Find: [tex]\frac{d}{dt} r(g(t))[/tex]
Solution:
Since, r(t) is composite function of g(t)
So, [tex]r(g(t))=<e^{4t+4} ,e^{4(4t+4)}, -4 >[/tex]
Thus, [tex]\frac{d}{dt} r(g(t))=<4e^{4t+4} ,16e^{16t+4} ,0>[/tex]
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