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
Differentiate e^cos x. The derivative of ecos x is -sin x ecos x. In this post, we will calculate the derivative of e to the power cos x by the first principle of derivatives as well as by the logarithmic differentiation and the chain rule of derivatives. We will also solve a few questions related … Read more
Derivative of tan x Formula
The derivative of esinx is equal to cosx esinx. Here we will calculate the derivative of e to the power sin x by the first principle, using the substitution method and the chain rule of derivatives. As an application, we will find the differentiation of several functions involving esin x. What is the derivative of … Read more
The derivative of 1/x is equal to -1/x2. The function 1/x (1 divided by x) is the reciprocal of x. In this article, we will find the derivative of 1/x using the power rule, product rule, and the definition of derivatives. What is the Derivative of 1/x? Answer: The derivative of 1/x is denoted by … Read more
The derivative of sin 3x is cos 3x. In this article, we will find the derivative of sin 3x by the substitution method, the chain rule, and the limit definition. Derivative of sin 3x Formula The formula of the derivative of sin 3x is given below. The following method will be used to prove the above … Read more
Derivative of sine inverse x. In this article, we will find the derivative of sin inverse x using the substitution method and the limit definition. In the end, we will evaluate the derivative of sine inverse 1/x as an application. What is the Derivative of Sin Inverse x? (Substitution Method) Step 1: Let y=sin-1 x … Read more
