Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. (3x + 3y)³ = 27x³ + 27y³, (-1, 1) Step 1 Expand the term (3x + 3y)³ in (3x + 3y)³ = 27x³ + 27y³ and simplify. (3x + 3y)³ = 27x³ + 27y³ 27x³ + 81x²y + 81xy² + 27y³ = 27x³ + 27y³ 81x²y + 81xy² x²y + = = 0

Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
(3x + 3y)³ = 27x³ + 27y³,
(-1, 1)
Step 1
Expand the term (3x + 3y)³ in (3x + 3y)³ = 27x³ + 27y³ and simplify.
(3x + 3y)³ 27x³ + 27y³
27x³ + 81x²y + 81xy² + 27y³ = 27x³ + 27y³
81x²y + 81xy²
Submit
Ski
x²y +
you
=
=
= 0
X
Transcribed Image Text:Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. (3x + 3y)³ = 27x³ + 27y³, (-1, 1) Step 1 Expand the term (3x + 3y)³ in (3x + 3y)³ = 27x³ + 27y³ and simplify. (3x + 3y)³ 27x³ + 27y³ 27x³ + 81x²y + 81xy² + 27y³ = 27x³ + 27y³ 81x²y + 81xy² Submit Ski x²y + you = = = 0 X
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Follow-up Question
Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
(3x + 3y)³ = 27x³ + 27y³,
(-1, 1)
Step 1
Expand the term (3x + 3y)³ in (3x + 3y)³ = 27x³ + 27y³ and simplify.
(3x + 3y)³ = 27x³ + 27y³
27x³ + 81x²y + 81xy² + 27y³ = 27x³ + 27y³
Step 2
x²y +
81x²y + 81xy² 10
=
x²y' + 2xy +
ху .y²
= 0
Differentiate the equation x²y + xy² = 0 with respect to x and solve for y'.
x²y + xy² = 0
y' + y² = 0
(x² + 2xy)y' =
Submit Skip (you cannot come back)
y'
=
=
0
−(y² + 2xy)
−(y² + 2xy)
(x² + 2xy)
X
Transcribed Image Text:Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. (3x + 3y)³ = 27x³ + 27y³, (-1, 1) Step 1 Expand the term (3x + 3y)³ in (3x + 3y)³ = 27x³ + 27y³ and simplify. (3x + 3y)³ = 27x³ + 27y³ 27x³ + 81x²y + 81xy² + 27y³ = 27x³ + 27y³ Step 2 x²y + 81x²y + 81xy² 10 = x²y' + 2xy + ху .y² = 0 Differentiate the equation x²y + xy² = 0 with respect to x and solve for y'. x²y + xy² = 0 y' + y² = 0 (x² + 2xy)y' = Submit Skip (you cannot come back) y' = = 0 −(y² + 2xy) −(y² + 2xy) (x² + 2xy) X
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