2.6 Implicit Differentiation
taxi Graph x²+y2=16. Is yu
a function of x?
محمد
y is not a function
a function y²=16-x
of X.
Y = √16x2
Пох
中
J=16-x²
Пож
+
と
These are explicit functions
• x² + y² = 16 implicitly deties y as a function x
と
"We can still consider targent lines of this curve
учусь
E-Key illen
dy
a) Find . £x (x²+y2) = $(16)
dx
M
2x + 2y = 0
the
14 - -2x
M
dy = -2x
こ
* (y²) = x (4165]²)
2[g] y'us
Chein rule.
= 2y 2
妥
гу
ly = -x
dx
y
2
b) Find equation of tangent line @ (-253,-2)
Note, x = xy² = (2013) (-2)² = 16 So, (-255,-L) is cipaint
| (213;12) = (23) = -√
√ +2 = √3(x+2√3)
the curve
on
У
=-√xx-6-2y=-53x-8
taxi Graph x²+y2=16. Is yu
a function of x?
محمد
y is not a function
a function y²=16-x
of X.
Y = √16x2
Пох
中
J=16-x²
Пож
+
と
These are explicit functions
• x² + y² = 16 implicitly deties y as a function x
と
"We can still consider targent lines of this curve
учусь
E-Key illen
dy
a) Find . £x (x²+y2) = $(16)
dx
M
2x + 2y = 0
the
14 - -2x
M
dy = -2x
こ
* (y²) = x (4165]²)
2[g] y'us
Chein rule.
= 2y 2
妥
гу
ly = -x
dx
y
2
b) Find equation of tangent line @ (-253,-2)
Note, x = xy² = (2013) (-2)² = 16 So, (-255,-L) is cipaint
| (213;12) = (23) = -√
√ +2 = √3(x+2√3)
the curve
on
У
=-√xx-6-2y=-53x-8
