Product Rule Differentiation

The product rule differentiation is used in differential calculus to help calculating the derivative of products of functions. The formula for the product rule differentiation is written for the product of two or more functions. If $u(x)$ and $v(x)$ are two functions of $x$ and $f(x)=u(x)v(x)$, then $$f^{\prime}(x) = u^{\prime}(x)v(x) + u(x)v^{\prime}(x)$$ Alternatively if \$y=u […]

Implicit Differentiation

This very powerful differentiation process follows from the chain rule.$$u = g(f(x)) \\frac{du}{dx} = g'(f(x)) \times f'(x)$$We’ve done quite a few differentiation and derivatives, but they all have been differentiation of functions of the form $y = f(x)$. Not all the functions will fall into this simple form. The process that we are […]

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 in order to achieve the valid solution of the differential equations, such as product rule, quotient rule and chain rule particularly.Many students missed applying the chain rule […]