Derivative

Derivative of xe^-x by First Principle & Product Rule

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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

Derivative of 1/x^2 by First Principle

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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

[Solved] What is the Derivative of 1/(1+x^2)?

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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

Derivative of e^x^2 by First Principle and Chain Rule

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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

Derivative of sin^2x by First Principle | sin^2x Derivative

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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

Epsilon Delta Definition of Limit | Negation of Epsilon Delta Definition

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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

Derivative of root(x)-1

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The derivative of root x minus 1 is 1 by 2 root x. In this post, we will prove this derivative formula by the power rule of derivatives as well as by the first principle of derivatives. Derivative of root(x)-1 Formula The Formula for the derivative of root x -1 is given below: Derivative of … Read more

Derivative of xsinx by First Principle

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The derivative of xsin x is sin x+x cos x. In this post, we will find the differentiation of x sin x using the first principle of derivatives. The derivative formula of xsin x is given below: $\dfrac{d}{dx}(x \sin x)$ $=\sin x+x\cos x$. We will now prove the above formula. Derivative of xsin x by … Read more