Find the values of x for which f(x) = xˣ, x > 0 is increasing.

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

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

Logarithmic Differentiation Technique, Increasing Functions and Their Properties | PadhAiPro

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TextLogarithmic Differentiation TechniqueIncreasing Functions and Their Properties

Let f(x) be a continuous function on [a, b] and differentiable on (a, b). Then, this function f(x) is strictly increasing in (a, b) if

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

Logarithmic Differentiation Technique

Derivative of Functions in Parametric Form

If y = (tan x)ˣ, then find dy/dx.

The function f(x) = x³ – 3x² + 12x – 18 is :

Show that f(x) = eˣ – e⁻ˣ + x – tan⁻¹ x is strictly increasing in its domain.

Find the intervals in which the function f(x) = log x/x is strictly increasing or strictly decreasing.