Simplify the following expression: (1 point) 2x − 2y + 5z − 2x − y + 3z
2 answers:
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Answer:
A.
Step-by-step explanation:
A. The problems asked for 2 ways to solve it, expanding the equation with the substitution x(t)=2 cos(t) and y(t)=4 sin(t) to differentiate it . The other way is by chain rule.
Expanding and differentiating:
We start by substituting x(t)=2 cos(t) and y(t)=4 sin(t) in h(x,y)=4x2+y2:
So, in the path that the hiker chose:
Chain rule:
We start differentiating h(x,y) using chain rule as follows:
Now, it´s easy to find all these derivatives:
Now we replace them in the chain rule, with the replacement x=2cos(t) and y=4sin(t) in the x,y that are left and we operate everything:
This will be our answer