This article will walk you through how to prove the Power Rule and take the derivative of any polynomial. We are going to prove every step of the way. If you don’t want to see the proof and just want a formula, then just know that for any function $f(x) = x^n$, $f'(x) = nx^{n-1}$;…
Read articleHello everyone! Today we will walk you through how to take the integral of $\csc(x)$. This is a highly unintuitive integral that cannot be solved by normal means, but $\csc(x)$ is also a very common function, so it’s important to know how to integrate it. The Integral First, we multiply the integrand of $\displaystyle\int\csc(x)\,dx$ by…
Read articleHello everyone! This article will walk you through how to take the integral of $x$. This is one of the most basic integrals, so it’s extremely important to know. Finding the Integral By the Fundamental Theorem of Calculus, $\displaystyle\dfrac{d}{dx} \int f(x)\,dx = f(x)$ for any continuous function $f(x)$. In other words, differention and integration are…
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