MTH311
Question: In calculus, the derivative of the composition of two or more functions is computed by one of the following rules.
Answer: The chain rule
Question: Given that \\(z=(2x+y^2 )^3, ∂z/∂y\\) equals
Answer: \\(6y–(2x+y^2)—^2\\)
Question: The converse of Euler’s theorem is
Answer: true
Question: \\((f°g)^\’ (c)\\) equals
Answer: \\f^\’ (g(c))∙g^\’ (C)\\)
Question: The entries of the Jacobian matrix are
Answer: partial derivatives.
Question: \\(d/dx(e^sinâ¡ã€–x^2 〗 )\\) equals
Answer: \\(e^sinâ¡–x^2 — cosâ¡–x^2 —2x\\)
Question: In number theory, Eulers theorem states that if n and a are co-prime positive integers, then
Answer: \\( a^(φ(n))≡1(modn)\\)
Question: Given that \\(z=lnâ¡–(2x^2+4y^2)—, ∂z/∂x equals\\)
Answer: \\(4x〖(2x^2+4y^2)—^(-1)\\)
Question: For\\( z=e^(3xy^2 ), ∂z/∂y\\) equals
Answer: \\(6xye^(3xy^2 )\\).
Question: The chain rule for total derivatives implies a chain rule for
Answer: partial derivatives
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