# Chain Rule Differentiation

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 […]

# Integration by Reverse Chain Rule

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 […]

# Finding a Function from Differential Equation

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 […]