promath The function e to the power x2 is written as $e^{x^2}$ and its derivative is $2xe^{x^2}$. In this post, we will find the derivative of e to the power x square by the first principle and chain rule of derivatives. Recall the first principle of derivatives: The derivative of a function f(x) by first principle … Read more
The derivative of 1 by root x is -1/(2x root(x)). In this post, we will find the derivative of 1/root(x) by the first principle of derivatives. We will also find the integration of 1 by root x. Derivative of 1 by root x from First Principle The first principle of derivatives says that the derivative … Read more
The function cos square x is the product of two cosine functions. The derivative of cos square x is equal to -sin2x. In this post, we will find the derivative of cos square x. Derivative of cos^2 x by First Principle The first principle of derivatives says that the derivative of a function f(x) is … Read more
The derivative of sin^2x by first principle is equal to 2sinx cosx=sin2x. Sin square x derivative is denoted by d/dx (sin2x) and its formula is given as follows: $\dfrac{d}{dx}$(sin2x) = 2sinx cosx = sin2x. In this post, we will find the derivative of sine square x. Derivative of sin square x by First Principle The … Read more
Note that the cosine function cos(x) is a trigonometric function. Here, we will learn about the domain, range, and period of cos(x). Domain of cos x One knows that for any value of x, the cosine function cos(x) is defined. Thus, by the definition of the domain of a function, we can say that the … Read more
The sine function sin x is a trigonometric function. In this post, we will learn about the domain, range, and period of sin x. Domain of sin x We know that the sine function sin x is computable for any real number x. Thus, the domain of sin x is the set of all … Read more
The quotient rule of limit says that the limit of the quotient of two functions is the same as the quotient of the limit of the individual functions. In this post, we will prove the quotient law of limit by the epsilon-delta method. Question: What is an epsilon-delta proof of the division rule of limit? Here, … Read more
The product rule of limits says that the limit of the product of two functions is the same as the product of the limits of the individual functions. In this post, we will prove the product law of limits by the epsilon-delta method. Question: What is an epsilon-delta proof of the product law of limits? … Read more
The sum rule of limits says that the limit of the sum of two functions is the same as the sum of the limits of the individual functions. In this post, we will prove the sum/addition rule of limits by the epsilon-delta method. Question: What is an epsilon-delta proof of the sum law of … Read more
The epsilon-delta definition of limit says that if limx→a f(x) = L, then for every ε>0, there exists a δ>0 such that |f(x)-L| < ε whenever 0<|x-a|<δ. In this post, we will learn the epsilon-delta definition of a limit with examples. We also provide the negative statement of the epsilon-delta definition of limits. Epsilon-Delta Definition of … Read more