Find the derivative of the vector function. r(t)=e^{t^{2}}i-j+\ln(1+3t)k

gabioskay7 2021-12-04 Answered
Find the derivative of the vector function.
r(t)=et2ij+ln(1+3t)k
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Expert Answer

George Burge
Answered 2021-12-05 Author has 16 answers
To find the derivative of r(t)=et2ij+ln(1+3t)k we will use Theorem 2 and Theorem 3 (differentiation rules). We have:
dr(t)dt=(et2)i1j+[ln(1+3t)]k
=et2(t2)i0j+11+3t(1+3t)k
=2tet2i+31+3tk
where we used the chain rule for the first and third component. We conclude that
dr(t)dt=2tet2i+31+3tk
Result:
dr(t)dt=2tet2i+31+3tk
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