Question

Tentukan dy/dx dari y = 1/sin^5 ( y-3x )

Answer 1

Menggunakan turunan parsial.
Notasi lain dari dy/dx adalah y'
y' = [d 1/sin⁵(y-3x)]/[d sin(y-3x)] . [d sin(y-3x)]/[d (y-3x)] . [d (y-3x)]/[dx]
y' = -5/sin⁴(y-3x). cos(y-3x). (y' - 3)
y'(1-(-5.cos(y-3x)/sin⁴(y-3x)) = -15cos(y-3x)/sin⁴(y-3x)
dy/dx = [-15cos(y-3x)/sin⁴(y-3x)]/[1+5cos(y-3x)/sin⁴(y-3x)]
dy/dx = [-15cos(y-3x)]/[sin⁴(y-3x)+5cos(y-3x)]