Derivatives up to order two of implicit functions

When dealing with implicit functions, we often have equations of the form: F(x, y) = 0 where y is an implicit function of x. That is, we can’t solve for y explicitly in terms of x. However, we can still differentiate the equation with respect to x to find the derivative of y with respect…

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Chain rule

The chain rule is a fundamental rule in calculus that allows you to differentiate a function that is composed of two or more functions. More specifically, if you have a function f(x) that is composed of two functions g(x) and h(x), such that f(x) = g(h(x)), then the chain rule states that: f'(x) = g'(h(x))…

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