## nth Derivative: Definition, Formula, Properties, Examples

The nth derivative of a function is obtained by the successive differentiation of the same function till n times. n-th differentiation is referred to the higher order derivatives. In this article, we will learn the definition of the nth derivative along with its formulas, properties, and examples. nth Derivative Definition Let f(x) be a differentiable … Read more

## Derivative of xlogx: Proof by First Principle, Product Rule

The derivative of xlog x is equal to 1+log x. Note that x log x is the product of x with its logarithm. In this post, we will learn how to find the derivative of xlog x. Derivative of xlogx Formula The formula for the derivative of xlogx is given as follows: d(xlogx)/dx = 1+logx. … Read more

## Derivative of xe^x: Proof by First Principle, Product Rule

The derivative of xex is equal to (x+1)ex. Note that xex is the product of two functions x and ex. In this post, we will find the derivative of xex by the first principle and the product rule of derivatives. Derivative of xex Formula The formula for the derivative of xex is given by d(xex)/dx … Read more

## Derivative of xcosx [by First Principle & Product Rule]

The derivative of xcos x is equal to cosx – xsinx. The function xcos x is the product of x with its cosine. In this article, we will learn how to find the differentiation of xcos x using the following methods: Product rule of derivatives First principle of derivatives. Derivative of xcosx Formula The derivative … Read more

## Derivative of 1/x^2: Formula, Proof [First Principle]

The derivative of 1/x2 is equal to -2/x3. Note that 1/x2 is an algebraic function. In this article, we will learn how to find the derivative of 1 divided by x2 using the power rule, product rule, and the definition of derivatives. Derivative of 1/x2 Formula The derivative of 1/x2 can be expressed as d/dx(1/x2) … Read more

## Derivative of 1 | Differentiation of 1

The derivative of 1 is zero. Note that 1 can be treated as a constant function. In this blog post, we will learn how to find the derivative of the constant 1 using different methods. Derivative of 1 Formula The natural number 1 is a constant. As the derivative of a constant is 0, we … Read more

## Derivative of e^-3x

The function e to the power -3x is written as e-3x and its derivative is -3e-3x. Here, we will find the derivative of e-3x by the following methods: Logarithmic differentiation Chain rule of differentiation First principle of derivatives. Derivative of e-3x Formula The derivative of e-3x is -3e-3x. Mathematically, we can express it as follows: d/dx(e-3x) = … Read more

## Derivative of e^-2x

The function e to the power -2x is an exponential function, denoted by e-2x. The derivative of e-2x is equal to -2e-2x. In this post, we will learn how to find the derivative of e-2x by the following methods: Logarithmic differentiation Chain rule of differentiation First principle of derivatives. Derivative of e-2x Formula The derivative of … Read more

## Derivative of log 5x | Derivative of ln 5x

The logarithm of 5x is denoted by log(5x) and its derivative is 1/x if the base is e. Here we will learn how to find the derivative of log(5x) with any base. The below methods will be used: Implicit function differentiation First principle of derivatives Chain rule of derivatives. Derivative of log 5x Formula The … Read more

## Derivative of log 4x | Derivative of ln 4x

The logarithm of 4x is denoted by log(4x) and its derivative is 1/x if the base is e. In this post, we will learn how to find the derivative of log(4x) with any base. The following methods will be used: Implicit function differentiation First principle of derivatives Chain rule of derivatives. Derivative of log 4x … Read more