Question
[Implicit Differentiation]
(5x-y)^4 + 2y^3 = 258 evaluate y' at the point (1,1)
(5x-y)^4 + 2y^3 = 258 evaluate y' at the point (1,1)
Answers
MathMate
Check that the point (1,1) satisfies the given equation, i.e. it is on the curve.
Use implicit differentiation to differentiate each term and obtain an equation containing x, y and y'.
Solve for y'.
You should get
y'=20(5x-y)³/(4(5x-y)³-6y²)
Substitute (1,1) into the above equation to get y'(1,1)=128/25.
Check my calculations.
Use implicit differentiation to differentiate each term and obtain an equation containing x, y and y'.
Solve for y'.
You should get
y'=20(5x-y)³/(4(5x-y)³-6y²)
Substitute (1,1) into the above equation to get y'(1,1)=128/25.
Check my calculations.
Z32
Thanks. Correct.
MathMate
You're welcome!