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
What is the Derivative of e2x? The derivative of e2x is 2e2x. Here, we will find the derivative of e2x using the derivative of ex. We will use three methods: substitution method, chain rule, and limit definition. Derivative of e2x Formula The derivative of e2x is 2e2x. This can be written mathematically as follows: d/dx(e2x) = 2 e2x … Read more
Derivative of x1/3. In this article, we will find the derivative of the cube root of x by applying the power rule of derivatives. We will also use the limit definition to evaluate the derivative of the cube root of x. What is the derivative of cube root of x? First Method of Finding Derivative of … Read more
Derivative of root x. The square root of x is an important function in mathematics. So it is natural to study the derivative of the square root of x. We will use the formula of power rule of derivatives to find it. We will also evaluate the derivative of the square root of x by … Read more
In this section, we will learn the derivative formulas of the inverse trigonometric functions with their proofs. Now we calculate the derivative of $\sin^{-1}x$ (or arc sin x). Derivative of $\sin^{-1}x$ \[\frac{d}{dx}(\sin^{-1}x)=\frac{1}{\sqrt{1-x^2}} \, (|x|<1)\] Proof: Note that $\sin^{-1}x$ is defined when $|x| \leq 1.$ We assume that \[y=\sin^{-1}x.\] As $|x| \leq 1$, we must have … Read more