The function f(x) = x |x|, x ∈ R is differentiable

Question

MCQ (Single)Differentiability and ContinuityCBSE PYQ

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Which of the following statements is true for the function f(x) = {x² + 3, x ≠ 0; 1, x = 0} ?

Check whether the function f(x) = x² |x| is differentiable at x = 0 or not.

Derivative of a Function

Differentiability and Continuity

If y = √(tan √x), prove that √x (dy/dx) = (1 + y⁴)/(4y).

If x = e^(x/y), prove that dy/dx = (log x – 1)/(log x)²

Check the differentiability of f(x) = {x² + 1, 0 ≤ x < 1; 3 – x, 1 ≤ x ≤ 2} at x = 1.

Check for differentiability of the function f defined by f(x) = |x − 5|, at the point x = 5.