what is implicit differentiation

what is implicit differentiation

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Implicit differentiation is a technique used to find the derivative of a function that is not written explicitly in terms of one of its variables, usually y in terms of x. Instead, the function is given implicitly as an equation involving both x and y. To perform implicit differentiation, we differentiate each side of the equation with respect to x, treating y as a function of x and using the chain rule to differentiate y terms. This allows us to find the derivative of y with respect to x, or dy/dx, even when we cannot solve for y explicitly. Implicit differentiation is useful in cases where the function is difficult or impossible to solve for y explicitly, such as when the equation is a circle or involves trigonometric functions.

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