Derivatives - Page 7

Derivative of 4e^x

This 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…

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Derivative of 1

To find the derivative of 1, we will start by graphing the equation $y = 1$, pictured below:   The derivative of a function at a point is the rate of change of a function at said specific point. In other words, it is the slope of the tangent line to the curve at a…

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Derivatives of Exponential Functions

Have 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…

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Derivative of xsinx

To find the derivative of \( x\sin x \) we will need to use the product rule. Furthermore, we will also need to recall the derivatives of $x$ and $\sin x$. Specifically, $$\dfrac d{dx} x = 1$$ and $$\dfrac d{dx}\sin x = \cos x$$ If you would like a refresher on how to find the…

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