If y√(x² + 1) = log(√(x² + 1) − x), show that (x² + 1) dy/dx + xy + 1 = 0.

Free previous-year papers & practice for JEE, NEET and CBSE Boards.

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Derivative of a Function, Derivative of Logarithmic Functions, Logarithmic Differentiation Technique | PadhAiPro

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TextDerivative of a FunctionDerivative of Logarithmic FunctionsLogarithmic Differentiation Technique

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

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

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

If √(1 – x²) + √(1 – y²) = a (x – y), prove that dy/dx = √(1 – y²)/√(1 – x²).

If y = (tan x)ˣ, then find dy/dx.

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