Inverse Trigonometry Continuity and Differentiability

Find dy/dx

(c) x^y + y^x = 1

Prove that:

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

If x^myⁿ = (x + y)^m+n, prove that

If y = 3 cos(logx) + 4 sin (logx), show that x²y₂ + xy₁ + y = 0

Differentiate

Differentiate the functions:

Differentiate the functions:

Find dy/dx

(b) (cosx)^y = (cosy)^x

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

If siny = x sin (a + y), prove that

Find dy/dx:

(a) xy = e^(x-y)

Differentiate the functions:

If If y = e^acos–1_x, -1 ≤ x ≤ 1, show that

If x^y = e^x-y, show that