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Differentiate the functions:

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

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

Differentiate

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

Prove that:

Find dy/dx:
(a) xy = e(x-y)
If If y = eacos–1x, -1 ≤ x ≤ 1, show that

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

If

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

Differentiate the functions:

If xy = ex-y, show that
