Equation 5 is a formula for the derivative d y / d x of a function defined implicitly by an equation F ( x , y ) = 0 , provided that F is differentiable and F y ≠ 0 . Prove that if F has continuous second derivatives, then a formula for the second derivative of y is d 2 y d x 2 = − F x x F y 2 − 2 F x y F x F y + F y y F x 2 F y 3
Equation 5 is a formula for the derivative d y / d x of a function defined implicitly by an equation F ( x , y ) = 0 , provided that F is differentiable and F y ≠ 0 . Prove that if F has continuous second derivatives, then a formula for the second derivative of y is d 2 y d x 2 = − F x x F y 2 − 2 F x y F x F y + F y y F x 2 F y 3
Equation 5 is a formula for the derivative
d
y
/
d
x
of a function defined implicitly by an equation
F
(
x
,
y
)
=
0
, provided that
F
is differentiable and
F
y
≠
0
. Prove that if
F
has continuous second derivatives, then a formula for the second derivative of
y
is
d
2
y
d
x
2
=
−
F
x
x
F
y
2
−
2
F
x
y
F
x
F
y
+
F
y
y
F
x
2
F
y
3
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
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