promath The derivative of cos cube x (cos^3x) is equal to -3cos2x sinx. In this post, we will find the derivative of cos cube x using the chain rule. The derivative formula of cos3x is given as follows: d/dx (cos3x) = -3cos2x sinx. Derivative of Cos^3x The derivative of cos3x is -3cos2x sinx. Explanation: As cos3x … Read more
The cos^3x formula is given by cos3x = (cos3x + 3cosx)/4. In this post, we learn how to prove the cos cube x formula. What is cos cube x formula Answer: cos3x=(cos3x + 3cosx)/4 is the formula of cos cube x. Proof: We will follow the below steps in order to prove cos cube x … Read more
The sin cube x formula is given as follows: sin3x = (3sinx -sin3x)/4, that is, sin^3x formula is equal to (3sinx – sin3x) divided by 4. Here we establish the formula of sine cube x and give a proof. What is sin cube x formula Answer: sin3x = (3sinx -sin3x)/4 Proof: To establish the formula … Read more
Sin3x formula in terms of cosx is expressed as follows: sin3x = (4cos2x-1)√(1-cos2x). Here we learn how to prove sin3x formula in terms of cosine of x. sin3x in Terms of cos x In order to express sin3x formula in terms of cosx, we will use the following trigonometric formulae: Using the above formulas, we … Read more
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