Find ∂ z / ∂ x and ∂ z / ∂ y by implicit differentiation, and confirm that the results obtained agree with those predicted by the formulas in Theorem 13.5.4. x 2 − 3 y z 2 + x y z − 2 = 0
Find ∂ z / ∂ x and ∂ z / ∂ y by implicit differentiation, and confirm that the results obtained agree with those predicted by the formulas in Theorem 13.5.4. x 2 − 3 y z 2 + x y z − 2 = 0
Find
∂
z
/
∂
x
and
∂
z
/
∂
y
by implicit differentiation, and confirm that the results obtained agree with those predicted by the formulas in Theorem 13.5.4.
Find the directional derivative of f at the given point in the direction indicated by the angle 0.
f(x,y)=√xy, (1,3), 0 = π/6
a.
b.
C.
d.
e.
1/1 (3+√³)
4
1/2 (3+√3)
1²/ (√ 3 + √²³)
3
— (3+√3)
4
√3
+ (₁-4)
3
4
3
Find the relation of the derivative of y and y with respect to x, given that yx- y² = 3x
II.
2y-x
3-x
IN.
2x-y
3-y
V.
1+2y
3-y
I.
II.
1-2xy
x-2y
Find
and
by implicit differentiation, and confirm that the
results obtained agree with those predicted by the following theorem.
If the equation f(x,y,z) = c defines z implicitly as a differentiable
fe
az
function of x and y, and if
70, then
xg/fe
ду
az
az
and
af/@y
ze/fe
In(1+ z) + xy? + 8z = 1
az
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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