kosala1478
contestada

find
[tex] \frac{dy}{dx \: } of \: \frac{x {}^{2} }{a {}^{2} } + \frac{y {}^{2} }{b { }^{2} } = 1 \\ \\ if \: x = a \cos( \alpha \:) \: and \: \: y \: = b \sin( \alpha ) [/tex]
pls help me ​

Respuesta :

MathPhys

Answer:

dy/dx = -b/a cot α

Step-by-step explanation:

x² / a² + y² / b² = 1

Take derivative with respect to x.

2x / a² + 2y / b² dy/dx = 0

2y / b² dy/dx = -2x / a²

dy/dx = -b²x / (a²y)

Substitute:

dy/dx = -b²a cos α / (a²b sin α)

dy/dx = -b cos α / (a sin α)

dy/dx = -b/a cot α