9x^2-y^2=1

(a) find y' by implicit differentiation

(b) Solve the equation explicitly for y and differentiate to get y' in terms of x

(c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a)

Question

Mathematics

Eloise

19 March, 00:43

9x^2-y^2=1

(a) find y' by implicit differentiation

(b) Solve the equation explicitly for y and differentiate to get y' in terms of x

(c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a)

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Answers (1)

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Aussie · Answer 1

9x^2 - y^2 = 1

a.) 18x - 2y dy/dx = 0

2y dy/dx = 18x

dy/dx = 9x/y

b.) y^2 = 9x^2 - 1

y = √ (9x^2 - 1)

y' = 9x / √ (9x^2 - 1)

c.) substituting y = √ (9x^2 - 1) into solution for part a gives

dy/dx = 9x / √ (9x^2 - 1)

Thus the two solutions are consistent.

9x^2-y^2=1(a) find y' by implicit differentiation(b) Solve the equation explicitly for y and differentiate to get y' in terms of x(c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a)

9x^2-y^2=1

(a) find y' by implicit differentiation

(b) Solve the equation explicitly for y and differentiate to get y' in terms of x

(c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a)