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
The function e to the power -x is an exponential function, denoted by e-x. The derivative of e-x is equal to -e-x. In this post, we will learn how to find the derivative of e-x by different methods. Derivative of e-x Formula The derivative of e-x is -e-x. Mathematically, this can be expressed as follows: d/dx(e-x) = … Read more
Note that e3x is an exponential function. The derivative of e3x is 3e3x. To find the derivative of e3x, we will use the below methods: Derivative of e3x Formula The derivative of e3x is 3e3x. Mathematically, we can express it as d/dx(e3x) = 3e3x or (e3x)’ = 3e3x. What is the derivative of e3x? Answer: The derivative of … Read more
The “log” function denotes a logarithm with base 10 referred to as common logarithms. So log 2x = log10 2x. If the base is e, then loge 2x = ln 2x is called the natural logarithm. Here, we will find the derivative of log 2x and ln 2x with respect to x. We have: The … Read more
The function “log” usually denotes the common logarithm, that is, it is a logarithm with base 10. If no base is mentioned, then one should consider the default base 10. So we have log x = log10x. Note that the logarithm with base e is called the natural logarithm, denoted by ln. That is, logex … Read more