Class 12 Derivations and Applications

Derive the derivative of an inverse trigonometric function by converting it to a trigonometric equation and differentiating implicitly.

Differentiate composite expressions involving inverse trigonometric, exponential, and logarithmic functions using the chain rule.

Differentiate functions of the form [u(x)]^[v(x)] using logarithmic differentiation.

Compute first- and second-order derivatives of a parametrically defined function.

Solve board-style rate-of-change problems by expressing the required rate as a derivative with respect to time.

Determine the intervals on which a function is increasing or decreasing from the sign of its first derivative.

Locate and classify local maxima and minima using the first-derivative or second-derivative test.

Translate a word problem into a one-variable function and use derivatives to find its maximum or minimum value.