Q15 of 45 Page 1

If y = x^x, prove that

We have, y = x^x

Taking log of both sides, we get

log y = x logx

on differentiating w.r.t x, we get

Differentiating again w.r.t x, we get

Hence proved.

Using properties of determinants, prove that

Differentiate with respect to when x ≠ 0.

Find the intervals in which the function f(x) = 3x⁴ - 4x³ - 12x² + 5 is

(a) strictly increasing

(b) strictly decreasing

Find the equations of the tangent and normal to the curve x = a sin³ θ and y = a cos³ θ at

Evaluate:

If y = xx, prove that