Question

d/dx(sin⁻¹x+cos⁻¹x)=........(| x | <1),Select Proper option from the given options.
(a) 0
(b) 2/√1-x²
(c) 1/√1-x²
(d) does not exist

Answer 1

In the attachment I have answered this problem.   The solution of this problem is simple and easy to understand.   See the attachment for detailed solution

Answer 2

we have to find out the value of $\bf{\frac{d}{dx}(sin^{-1}x+cos^{-1}x)}$

definitely , if you know about concept of inverse trigonometric functions, you will get its answer just 1 second.

as you know, $sin^{-1}x+cos^{-1}x=\frac{\pi}{2}$
so, we can write π/2 in place of sin^-1x + cos^-1x .
so, $\bf{\frac{d}{dx}(sin^{-1}x+cos^{-1}x)=\frac{d}{dx}\{\frac{\pi}{2}\}}$

= 0 [ as we know ,π/2 is constant and derivative of constant function is zero.]

hence, answer is 0.
therefore, option (a) is correct