promath The formula of cosh2x-sinh2x is given by cosh2x-sinh2x =1. Here we will learn how to prove cosh^2x-sinh^2x=1. Before we prove the identity cosh2x-sinh2x=1, let us recall that Proof of cosh^2x-sinh^2x=1 Question: Prove that cosh2x-sinh2x =1. Answer: By the above two formulas, we have that L.H.S = cosh2x – sinh2x = $\Big(\dfrac{e^x+e^{-x}}{2} \Big)^2$ $- \Big(\dfrac{e^x-e^{-x}}{2} \Big)^2$ … Read more
The derivative of coshx, denoted by d/dx(coshx), is equal to sinhx. Here we will learn how to differentiate cosh(x), i.e, how to find the derivative of the hyperbolic cosine function with respect to x. The formula of the derivative of coshx is given below: d/dx[coshx] = sinhx. To find the differentiation of coshx, we will … Read more
The derivative of sinhx, denoted by d/dx(sinhx), is equal to coshx. In this post, we will learn how to differentiate sinh(x), i.e, how to find the derivative of the hyperbolic sine function with respect to x. The derivative formula of sinhx is given as follows: d/dx[sinhx] = coshx. Before differentiating sinh(x), let us first recall … Read more
The derivative of tanh(x), denoted by d/dx tanh(x), is equal to sech2x. In this post, we will learn how to differentiate tanh(x), i.e, how to find the derivative of the hyperbolic tan function with respect to x. The derivative formula of tanh(x) is given as follows: d/dx[tanh(x)] = sech2x. How to Differentiate tanh(x) As tanh … Read more
The integration of sec square x (sec2x) is equal to tanx+C. In this post, we learn how to integrate sec^2x. Sec^2x Integration Formula The integration formula of sec2x is given by ∫sec2x dx = tanx +C where C denotes an integral constant. What is the Integration of sec^2x Answer: The integration of sec^2x is tanx+C. … Read more
The integration of cot^2x is equal to -(cot x +x)+C. In this post, we will learn how to find the integral of cot^2x (cot square x). We will use the following two formulas: Find Integration of cot2x Question: Find the integration of cot2 x?That is, find ∫cot2 x dx. Answer: The integration of cot2x is … Read more
The integration of cos square x is x/2+(sin2x)/4+C, C is a constant. Here we learn how to integrate cos2x. The integration formula of cos square x is given as follows: ∫cos2x dx = x/2 +(sin2x)/4 +C where C is a constant. How to Integrate cos^2x First, we write down the trigonometric formula of cos2x. The … Read more
The integration of sin square x is equal to x/2 – (sin2x)/4 +C. Here we learn how to integrate sin2x. The integration of sin2x formula is given by ∫sin2x dx = x/2 – (sin2x)/4 +C where C is an arbitrary integral constant. How to Integrate sin^2x To integrate sin square x, we will use the … Read more
The integration of fourth root of x is 4×5/4/5 + C. In this post, we will find the integral of the fourth root of x by the power rule of integration. Let us now learn how to integrate fourth root x. Integral of Fourth Root of x The fourth root of x is expressed as … Read more
The derivative of cot^2x is -2cotx cosec2x. Here we find the derivative of cot square x by the first principle of derivatives. Differentiation of cot square x by the first principle will be computed as follows. Derivative of cot square x by First Principle By first principle, the derivative of f(x) is given by the … Read more