Inverse Trigonometry Continuity and Differentiability

Find dy/dx

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

If

Differentiate the functions:

Differentiate

Find the relationship between a and b so that the function  f defined by 

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

Prove that:

Verify Rolle’s Theorem for the function f, given by f(x) = e^x (sinx – cos x) on 

Find dy/dx:

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

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

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

If

Differentiate

Differentiate the functions:

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