The derivative at point is given by

Differentiation formulas

The product Rule

The Quotient Rule

Chain Rule

Implicit Differentiation

For functions which are defined implicitly, such as , we can differentiate both sides of the equation with respect to , applying the Chain Rule whenever necessary.

Logarithmic Differentiation

For some cases, such as , we cannot differentiate directly. We can do

Derivatives of Inverses

However, this result is only true for first-order derivatives. It doesn’t work for higher order derivatives.

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