October 8, 2024 - Page 2

1/x-1 Derivative

To find the derivative of $\dfrac{1}{x-1}$, we have to use the power rule and the chain rule. Step 1. Rewrite First, it is easier to rewrite $\dfrac{1}{x-1}$ as $(x-1)^{-1}$. This makes differentiation simpler because we can now apply the power rule directly. Step 2. Power Rule According to the power rule, $\dfrac{d}{dx} x^n = n…

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Derivative of a negative $x$

\[\begin{align*} \boxed{\displaystyle \frac{d}{dx} (-x) = -1} \end{align*}\] Let’s learn how to find the derivative of the function \( f(x) = -x \). Don’t worry—we’ll keep it simple and easy to understand! What is a Derivative? A derivative tells us how a function changes as the input \( x \) changes. Think of it like measuring how…

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Derivative of f(x)=x

\[\begin{align*} \boxed{\displaystyle \frac{d}{dx} (x) = 1} \end{align*}\] Let’s learn how to find the derivative of the function $f(x) = x$. It’s simple, we will show every step. What is a Derivative? A derivative tells us how a function changes as the input $x$ changes. Think of it like finding out how fast or slow something is…

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Derivative of 4 ^ x or $4^x$

Introduction Hello everyone! In this article, we will review how to take the derivative of $4^x$. This is a very instructive example for how to take the derivative of an exponential function with a base other than $e$, which is a very important concept to understand. Without further ado, let’s get into it! Taking the…

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Integral of $\sin 2x$

Introduction Hello everyone! In this blog post, we will discuss how to take the integral of $\sin 2x$. This is important to know, because it touches on two important concepts – integrals of trigonometric functions and $u$-substitution. Integrals of Trig Functions We know that the derivative of $\sin x$ is $\cos x$, and the derivative…

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