Question

1.) (Please use exponent form instead of roots and leave negative exponents negative.) Use Implicit Differentiation to solve the following for : a.) y cos(x) = In(y) - x b.) x-1 y +2 y 1/2 = 5 x3 2.) Differentiate the following: a.) x2 cosh(x) b.) 5x + log (x) 3.) A plane moving at 600 km/hr passes directly above a radar station at an altitude of 5km. (Hint: Draw a diagram!) a.) How fast is the distance between the plane and the radar station changing 1 minute after the flyover? b.) How fast is the distance between the plane and the radar station changing at the moment of the flyover?

Answer 1

y cosa a day on Differentiating both side with pespect to n, we get f(y losa) = f (dny-a) (Y).cosa + y lon) da (any) - a (1) ay du cosa + y". (-sina) - t . dula 1 2y loss.dya + de la = -1 + y sina du lan (2 y losa - t) = yusinn - – da ( 24°C032.41 ) - yusina-1 CAS2 ylersina-i) 2 y Con- Therefore, a y (yesinx-1) 2 y losari (9) only + 2y = 523 Differentiating both side with respect ton, we get a la (aly + 2y²) na (523) - (a'y) + 2 dalyk) 5 fu (20)

2 of 1 (2.). y + 2". In (%) + 2 + y2 l dy = 5:32 -1.8ly t 21 de a + yoz dy = 15 20 - *?y tale om et yn de 159- (x + y - ₃) dy = 152 tazy 7 dien 15a+ way 152-t 2-1 ty z Therefore, de Ni+ y 2)