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In differential calculus, the chain rule is a formula for determining the derivative of the combined two or more functions. the chain rule could be used in Leibniz’s notation in the following way.If $y=g(u)$ where $u=f(x)$ then $\displaystyle \dfrac{dy}{dx}=\dfrac{dy}{du} \times \dfrac{du}{dx}$.Generally, the chain rule is described as following in its simplest understanding.If $y=\big[f(x)\big]^n$ then $\displaystyle […]
By recalling the chain rule, the Integration Reverse Chain Rule comes from the usual chain rule of differentiation. This skill is to be used to integrate composite functions such as\( e^{x^2+5x}, \cos{(x^3+x)}, \log_{e}{(4x^2+2x)} \).Let’s take a close look at the following example of applying the chain rule to differentiate and then reverse its order to […]
The solution of a differential equation is to find an expression without \( \displaystyle \frac{d}{dx} \) notations using given conditions.Note that the proper rules must be in place to achieve a valid solution of the differential equations, such as the product, quotient, and chain rules.Many students missed applying the chain rule, resulting in an unexpected […]