Inverse Trigonometry Continuity and Differentiability

Differentiate the following w.r.t. x:

If log (x² + y²) If

Differentiate the following w.r.t.x.

Differentiate the functions:

Let f

Determine the value of ‘a’, if possible, so that the function is continuous at x = 0.

If

If x¹⁶y⁹ = (x²+ y)¹⁷ prove that

Determine the values of a, b, and c for which the function

If y = log tan (π/4 + x/2), show that dy/dx= sec. Also find the value of d²y/dx² at x = π/4.

Find dy/dx

(b) (cosx)^y = (cosy)^x 

Find the values of k so that the function f is continuous at the indicated point 

If x = a(cost + tsint) and y = a (sint – tcost),

Show that the function f defined as follows, continuous at x = 2, but not differentiable thereat:

Differentiate the functions:

Show that the function f=(x)=|x-3|, x ϵ R, is continuous but not differentiable at x = 3.

If y = Ae^mx + Be^nx, show that

If

If

continuous at x = 2, find the value of k.

Find all the points of discontinuity of the function f(x) = [x²] on [1, 2), where [.] denotes the greatest integer function.

If x^myⁿ = (x + y)^m+n, prove that