promath The formula of cos^2x – sin^2x is equal to cos2x. Let us learn how to establish the proof the identity of cos2x-sin2x. cos2x-sin2x formula is given by cos2x-sin2x = cos2x. Proof of cos2x-sin2x Formula Question: Prove that cos2x-sin2x = cos2x. Proof: cos2x-sin2x = cosx ⋅ cosx – sinx ⋅ sinx = cos(x+x), here we have … Read more
The derivative of sinx/x is equal to (xcosx -sinx)/x2. Here we will learn how to differentiate sinx/x with respect to x. The derivative formula of sinx/x is given by $\dfrac{d}{dx}(\dfrac{\sin x}{x})$ = $\dfrac{x\cos x -\sin x}{x^2}$. Find the Derivative of sinx/x As sinx/x is a quotient function, to find the derivative of sinx/x we will … Read more
The integration of coshx is equal to sinhx+C. Here we learn how to integrate coshx, the cosine hyperbolic function. The integration formula of cosh(x) is given as follows: ∫coshx dx = sinhx +C where C denotes an integral constant. How to Integrate coshx Question: What is the integral of coshx? That is, Find ∫coshx dx. … Read more
The integral of sinhx is equal to coshx+C. Here we learn how to integrate sinhx, the sine hyperbolic function. The sinh(x) integral formula is given below: ∫sinhx dx = coshx +C where C is an integration constant. How to Integrate sinhx Question: Find the integral of sinhx, that is, Find ∫sinhx dx. Answer: One know … Read more
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