Hello everyone! This article will walk you through how to take the derivative of $3x$, and also any polynomial. Not only will we do this, but we will also 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…
Read articleIntegrals and derivatives of trigonometric functions can be tricky. You may have been told in your math class that $\dfrac{d}{dx} \sin(x) = \cos(x)$, but not given a good explanation for it. In this article, we will show you the derivatives and integrals of all the trigonometric functions while also proving that they are true. Derivatives…
Read articleThis article will teach you how to take the derivative of $4e^x$, as well as the proof for why the derivative is correct. Taking the Derivative Let us take the derivative of $\ln e^x$. Of course, $\ln e^x = x$, so the derivative should equal $1$. Using the chain rule, we get that $\frac{d}{dx} \ln…
Read articleTo find the derivative of 1, we will start by graphing out the equation $y = 1$, pictured below: We define the derivative of a function at a specific point as the rate of change of a function at said specific point. In other words, it is the slope of the tangent line to the…
Read articleHave you ever wondered how to take the derivative of an exponential function like \(2^x\) or \(4^{3x^2}\)? In this article, we will derive the formula for taking the derivative of any exponential function whatsoever. Derivation of the Formula In order to derive the formula for the derivative of an exponential function, we first need to…
Read articleTo find the derivative of \( x\sin x \) we will need to use the Product Rule, Power Rule on \( x \), and the derivative of \( \sin x \). By the Product Rule, \( (fg)’=f’g+g’f \). By the Power Rule, the derivative of \( x \) is equal to \( 1 \). The…
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