Question

EXAMPLE 1 (a) If x^2 + y^2 = 100, find dy/dx. (b) Find an equation of the tangent to the circle x^2 + y^2 = 100 at the point (8, 6). SOLUTION 1 (a) Differentiating both sides of the equation x^2 + y^2 = 100: d/dx ( [ ] ) = d/dx (100) d/dx ( [ ] ) + d/dx (y^2) = 0. Remembering that y is a function of x and using the Chain Rule, we have d/dx (y^2) = d/dy ( [ ] ) dy/dx = [ ] dy/dx Thus 2x + [ ] dy/dx = 0. Now we solve this equation for dy/dx: dy/dx = [ ]. (b) At the point (8, 6) we have x = 8 and y = 6, so dy/dx = [ ]. An equation of the tangent to the circle at (8, 6) is therefore y - [ ] = [ ] (x - [ ]) or [ ]

          EXAMPLE 1
(a) If x^2 + y^2 = 100, find dy/dx.
(b) Find an equation of the tangent to the circle x^2 + y^2 = 100 at the point (8, 6).
SOLUTION 1
(a) Differentiating both sides of the equation x^2 + y^2 = 100:
d/dx ( [ ] ) = d/dx (100)
d/dx ( [ ] ) + d/dx (y^2) = 0.
Remembering that y is a function of x and using the Chain Rule, we have
d/dx (y^2) = d/dy ( [ ] ) dy/dx = [ ] dy/dx
Thus
2x + [ ] dy/dx = 0.
Now we solve this equation for dy/dx:
dy/dx = [ ].
(b) At the point (8, 6) we have x = 8 and y = 6, so
dy/dx = [ ].
An equation of the tangent to the circle at (8, 6) is therefore
y - [ ] = [ ] (x - [ ])
or
[ ]

EXAMPLE 1
(a) If x^2 + y^2 = 100, find dy/dx.
(b) Find an equation of the tangent to the circle x^2 + y^2 = 100 at the point (8, 6).
SOLUTION 1
(a) Differentiating both sides of the equation x^2 + y^2 = 100:
d/dx ( [ ] ) = d/dx (100)
d/dx ( [ ] ) + d/dx (y^2) = 0.
Remembering that y is a function of x and using the Chain Rule, we have
d/dx (y^2) = d/dy ( [ ] ) dy/dx = [ ] dy/dx
Thus
2x + [ ] dy/dx = 0.
Now we solve this equation for dy/dx:
dy/dx = [ ].
(b) At the point (8, 6) we have x = 8 and y = 6, so
dy/dx = [ ].
An equation of the tangent to the circle at (8, 6) is therefore
y - [ ] = [ ] (x - [ ])
or
[ ]

Added by Christopher N.

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