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
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
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: Derivative of xcosx Formula The derivative of xcosx formula is given by d(xcosx)/dx = … Read more
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
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
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
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
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
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
The derivative of e4x is 4e4x. Note that e4x is an exponential function with exponential 4x. Here, we will find the derivative of e to the power 4x using the following rules: Logarithmic differentiation First principle of derivatives Chain rule of derivatives. Derivative of e4x Formula The derivative of e4x is 4e4x. Mathematically, we can write … Read more
