Multivariable Calculus 7 | Chain, Sum and Factor rule

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Here we talk about the linearity of differentiation and the chain rule for multivariable functions.

#MultivariableCalculus
#Analysis
#Integral
#Calculus
#Derivatives
#Mathematicspdt
#Lagrange

(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[YaoweiZhang]

Maybe a dumb question but why the last term, namely varphi_f(h_1)/||h|| approches zero if h approches zero? I am confused because phi is not necessarily a linear function hence we cannot pull the norm of h inside the parenthesis or pull the sum outside the parenthesis.

[rafaelschipiura]

Finally you summed two matrices. You defined a matrix sum in the linear algebra course and never used it. 😛