Question

32.. If y = x3 (cOS X)^x+ sin-1√ x, find dy/dx​

Answer 1

Answer:

Step-by-step explanation:

⇒y=(cos x)^x+(sin x)^1/x,

⇒=  u+v,

⇒u=(cos x)^x   &    v=(sin x)^1/x,

⇒Ln u,

=x Ln(cos x),

⇒1/u*d u/d x,

=1*Ln(cos x)+x*1/(cos x)  (- sin x),

⇒d u/d x,

=(cos x)^x [ Ln(cos x)-x tan x] ------- 1,

⇒Ln v,

=1/x Ln(sin x),

⇒1/u d v/d x,

=-1/x²*Ln(sin x)+1/x 1/(sin x)  (cos x),

⇒d v/d x,

=(sin x)^11 x/x²[x cot x-Ln(sin x)]  --------- 2,

⇒y=u+v,

⇒d y/d x,

=d u/d x+d v/d x,

⇒d y/d x,

=(cos x)^x[Ln(cos x)-x tan x]+(sin x)^1/x/x²[x cot x-Ln sin x],

Hope it helps.