Q11 of 147 Page 183

If y = 5 cos x – 3 sin x, prove that

It is given that y = 5 cos x – 3 sin x

Now, on differentiating we get,

= 5(-sinx) – 3(cosx)

= -(5sinx + cosx)

Then,

= - [5cosx +3(-sinx)]

= -[5cosx-3sinx]

= -y

Therefore,

Hence Proved.

Find the second order derivatives of the function

log (log x)

Find the second order derivatives of the function

sin (log x)

If y = cos^–1 x, Find d²y/dx² in terms of y alone.

If y = 3 cos (log x) + 4 sin (log x), show that x² y₂ + xy₁ + y = 0