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

Question

TextDerivative of a FunctionDifferentiability 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} ?

The derivative of sin (x²) w.r.t. x, at x = √π is :

Derivative of a Function

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

The derivative of tan⁻¹(x²) w.r.t. x is :

If f(x) = |tan 2x|, then find the value of f′(x) at x = π/3.

If y = cosec(cot⁻¹ x), then prove that √(1 + x²) dy/dx – x = 0.