Product Rule of Probability: Probability Regarding AND

Transcript They give you the probability of a, b, c, and d in the question. Part a! They want us to find the probability of a and b. The probability of a and b is simply a probability of times the probability of b which becomes 1 on 24. And that’s it, guys. That’s pretty […]

Product Rule Differentiation

The product rule differentiation is used in differential calculus to help calculate 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$$\large f^{\prime}(x) = u^{\prime}(x)v(x) + u(x)v^{\prime}(x)$$Alternatively if \$y=u \times […]

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 all have been the differentiation of functions of the form $y = f(x)$. Not all functions will fall into this simple form. The process that we are going […]

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 […]