Let y=(logx)^x+ x^xcosx. Then find .

OR

If x= a sin(pt), y=b cos(pt). Then find at t = 0.

Given Data:

y=(logx)^x+ x^xcosx

Let u = (logx)^x and v = x^xcosx

Considering u = (logx)^x

Taking log,

logu = x log(logx)

Differentiating w.r.t x,

Considering v = x^xcosx

Taking log,

⇒ logv=x cosx logx

Differentiating w.r.t x,

Now y = u + v

Using the above values,

OR

Given Data:

x= a sin(pt), y=b cos(pt)

Differentiating w.r.t t

Now divide 2^nd equation with 1^st, we get

Again differentiating w.r.t x we get

Using the above value, we get

At t = 0, sec 0 =1