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
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