promath The cube root of x is an algebraic function. In this article, we will learn its definition, graph, various properties, etc. We will also learn how to find its derivative and integration. Cube Root Definition If A3 =x, then the number A is called a cube root of x. Symbolically, we can write it as … Read more
The square root of x is an algebraic function. It is denoted by the symbol $\sqrt{x}$. In this article, we will learn its definition, graph, various properties, etc. We will also learn how to find its derivative and integration. Square Root Definition If $B^2=x$, then we say that the number $B$ is a square root … Read more
The derivative of x3 cosx is equal to 3x2cosx – x3sinx. The function x3cosx is the product of two functions x cube and cosx. In this post, we will find the derivative of x3cosx. What is the Derivative of x3cosx? Answer: The derivative of x3cosx is equal to 3x2cosx-x3sinx. Explanation: We will use the product … Read more
The derivative of 1/log x is -1/x(log x)^2. Note that 1/logx is the reciprocal of logx. In this post, we will learn how to find the derivative of 1 divided by log x. What is the Derivative of 1/logx? Answer: The derivative of $1/\log x$ is $-\dfrac{1}{x(\log x)^2}$. Explanation: Step 1: Let $z = 1/\log … Read more
The derivative of x^3 is equal to 3x^2. The function x3 denotes the cube of x. In this post, we will find the derivative of x cube by different methods; for example, by the power rule, by the limit definition of derivatives. Derivative of x3 by Power Rule To find the derivative of x cube, … Read more
The derivative of x is equal to 1. The function f(x)=x denotes the identity function on the set of real numbers. In this post, we will find the derivative of x by different methods; for example, by power rule, by the limit definition of derivatives. Derivative of x by Power Rule We will use the … Read more
The derivative of x2 (x square) by first principle is 2x. The function x2 denotes the square of x. In this post, we will find the derivative of x square. The derivative of x square is denoted by d/dx (x2), and its formula is given below: $\dfrac{d}{dx}$ (x2) = 2x. Derivative of x2 by First … Read more
The derivative of xe-x is equal to (1-x)e-x. In this post, we will find the derivative of xe^-x by the product rule and the first principle of derivatives. Derivative of xe-x by First Principle The derivative of $f(x)=xe^{-x}$by the first principle is given by $(xe^{-x})’$ = limh→0 $\dfrac{(x+h)e^{-(x+h)}-xe^{-x}}{h}$ = limh→0 $\dfrac{xe^{-(x+h)}+he^{-(x+h)}-xe^{-x}}{h}$ = limh→0 $\big(\dfrac{xe^{-(x+h)}-xe^{-x}}{h}$ $+\dfrac{he^{-(x+h)}}{h} … Read more
The derivative of 1 by x square is equal to -2/x3. In this blog post, we will learn how to find the differentiation of 1/x2. What is the Derivative of 1/x2? Let us now find the derivative of 1/x^2 by the power rule of derivatives. The power rule says that $\dfrac{d}{dx}(x^n)=nx^{n-1}$ Step 1: First,we write … Read more
The derivative of 1 by 1+x^2 is equal to -2x/(1+x^2)^2. In this post, we find the derivative of 1/(1+x^2) using the chain rule and substitution method. Derivative of 1/(1+x^2) Let us find the derivative of 1/(1+x^2) by the substitution method and the product rule of derivatives. Suppose that $u=\dfrac{1}{1+x^2}$ …(I) We will need to find … Read more