Let c1(t) = eti + (sin(t))j + t3k and c2(t) = e−ti + (cos(t))j − 6t3k. Find the stated derivatives in two different ways to verify the differentiation rules. d dt [c1(t) + c2(t)]

Step-by-step explanation:

Step 1:-

Given c1(t) = e^ t i + (sin(t))j + t^3k

and c2(t) = e^−t i + (cos(t))j − 6t^3k.

adding c1(t)+c2(t) = e^ t i + (sin(t))j + t^3k+ e^−t i + (cos(t))j − 6t^3k

by using derivative formula

now differentiating with respective to 't'

taking common i, j and k terms ,we get

its the second choice.

step-by-step explanation:

the elements in the range will be 7 less than the elements in the domain.