Calculus

Answer: The derivative of e^2x by first principle is equal to 2e2x. In this article, we will find the derivative of e to the power 2x using the first principle. Recall that for a function f(x) in one variable x, the derivative of f(x) from first principle is given by the limit below: $\dfrac{d}{dx}(f(x))$ $=\lim\limits_{h … Read more

The derivative of log3x is 1/x. In this post, we will find the derivative of log 3x by first principle. To do so, we will use the following limit formula on logarithm functions: $\lim\limits_{x \to 0} \dfrac{\log(1+x)}{x}=1$ $\quad \cdots (i)$ Derivative of log 3x from First Principle The first principle of derivatives says that the … Read more

Derivative of root x: The square root of x is a very important function in Mathematics. In this post, we will find the derivative of the square root of x using the first principle of derivatives and by the power rule of derivatives. At first, we find the derivative of root x by limit definition, … Read more

The derivative of e3x is 3e3x. The function e^3x is an exponential function with an exponent 3x. In this note, we will find the derivative of e to the power 3x by the first principle of derivatives and by the chain rule of derivatives. Derivative of e^3x using first principle As we know that the derivative … Read more

Note that the square root of 1+x can be written as (1+x)1/2. In this post, we will find the derivative of the square root of 1+x by the first principle of derivatives. Using this principle, the derivative of a function f(x) is $\dfrac{d}{dx}(f(x))$ $=\lim\limits_{h \to 0} \dfrac{f(x+h)-f(x)}{h}$ Derivative of sqrt(1+x) using Limit Definition Let $f(x)=\sqrt{1+x}$. … Read more

The function log(cos x) denotes the logarithm of the cosine function. Here we will find the derivative of log(cos x) using the first principle of derivatives. The derivative of a function $f(x)$ by the first principle of derivatives is defined to be the following limit: $f'(x)=\dfrac{d}{dx}(f(x))$ $=\lim\limits_{h \to 0} \dfrac{f(x+h)-f(x)}{h}$ $\quad \cdots (i)$ Here the symbol … Read more

If f(x) is a function of the real variable x, then its derivative by the first principle of the derivative is given by $f'(x)=\lim\limits_{h \to 0} \dfrac{f(x+h)-f(x)}{h}$ $\quad \cdots (i)$ Here $’$ denotes the derivative. In this post, we will find the derivative of \log(\sin x) by the first principle of derivatives. Derivative of log(sinx) … Read more

The derivative of square root of cosx is equal to (-sin x)/(2 root(cos x)).In this post, we will learn how to find the derivative of root cosx by first principle, that is, by the limit definition. The first principle of derivative is defined as follows: Let $f(x)$ be a differentiable function of $x$. The derivative … Read more

The derivative of $\tan x$ is $\sec^2 x$, that is, $\dfrac{d}{dx}(\tan x)=\sec^2 x$. In this post, we will learn how to find the derivative of tan x by the product rule of derivatives as well as the quotient and chain rule of derivatives. At first, we will recall the rules. Let $f(x)$ and $g(x)$ be two … Read more