Esercizi svolti di analisi reale e complessa - Dipartimento di ...

g : R −→ R
t ↦−→ tgh t + 1 + t 2
F (t) ≡ f(g(t), 1 − g 2 (t)) F ′ (0)
f ∈ C 1 (R 3 , R) h ∈ C 1 (R 2 , R)
∂
f(x, h(x, z), z) e
∂ x
∂
f(x, h(x, z), z) .
∂ z
y = f(x) C 2 x = 0
x 2 + sinh y + e xy = 1
f(0) = 0
x ∈ R2 y ∈ R3 f : R5 →
R6 f ∈ C1 ∂f
∂x ∂f
∂y
g : R → R3 C1 ∂
∂t f(x, g(t) )
f(x, y, t) = (sin(tx1), |x|, (y1+y2 2x3) 1+t )
x ∈ R3 ,
y ∈ R2 t ∈ R .
∂f ∂f
∂x , ∂y ∂f
∂t x = 0 t = −1
g(t) = (tanh t, ln[ln t] ), ∂
∂t [f(x, g(t), t)] x = 0
t > 1
f(x) = e |x|2
D1f(0) (ξ) D3f(0) (1, 2, .., n) 3
(x1 + x 4 n ) x ∈ R n