#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-5470-145

+91 7353221155

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

# Consider the function f(x) = sin-1(3x-4x3) + cos-1(4x3-3x)Let the dreivative of the function be, f'(x) = D1+D2where D1 = (d/dx)(sin-1(3x-4x3))   -------------(1)and D2 = (d/dx)(cos-1(4x3-3x))    ------------(2)Let x = sinθ so that (1) becomes;D1 = (d/dx)(sin-1(3sinθ-4sin3θ))ie, D1 = (d/dx)(sin-1(sin 3θ)ie, D1 = (d/dx)(3θ)ie, D1 = (d/dx) (3 sin-1 x)similarly, putting x = cos φ in (2), we can show thatD2 = (d/dx) (3 cos-1 x)Therefore, f'(x) = D1+D2= (d/dx) (3 sin-1 x) + (d/dx) (3 cos-1 x)= (d/dx)(3(sin-1 x+ cos-1 x)= (d/dx)(3π÷2)=0But, We can prove that the aboce given function f(x) is not a constant function either by substituting 3x-4x3 = y or using a scientific calculator!!!How this is possible? Can the derivative of a non-constant function be zero???

11 years ago
dude, there is no rule that the derivative of a function is not zero it is always zero for a constant function one thing is that you have definitely gone wrong when you have substituted 3theta for arcsin[sin[theta]] by the way may i know the values of your scientific calculator that has shown dif values Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear Davis Devasia

sin-1 x+ cos-1 x =∏/2

you can use this formula if x is same in both sin-1x and cos-1x

but here you can use it because x in sin-1x is sinΘ

and x in cos-1x is cosΦ   ,both are different .you can use this formula

Please feel free to post as many doubts on our discussion forum as you can.
If you find any question Difficult to understand - post it here and we will get you the answer and detailed
solution very  quickly.

All the best.

Regards,