promath The general solution of the differential equation dy/dx=cos(x+y) is equal to tan(x+y)/2 = x+C. Here we learn how to solve dy/dx=cos(x+y). Find General Solution of dy/dx=cos(x+y) Question: What is the solution of dy/dx=cos(x+y)? Answer: The solution of dy/dx=cos(x+y) is tan(x+y)/2 = x+C. Solution: Let x+y=2u So 1+ $\dfrac{dy}{dx}$ = 2 $\dfrac{du}{dx}$ ⇒ $\dfrac{dy}{dx}$ = 2 … Read more
The integration of sin^3x cos^2x is equal to (cos5x)/5 – (cos3x)/3 +C where C is a constant. Here we learn how to integrate sin^3x cos^2x. What is the Integration of sin3x cos2x? Question: Find the integral of sin3x cos2x, that is, Find ∫sin3x cos2x dx Solution: We have: ∫sin3x cos2x dx = ∫sin2x sin x … Read more
The derivative of x^logx (x to the power logx) is equal to 2 logx xlogx-1. Here we find the differentiation of xlogx by using the product rule of derivatives together with logarithmic differentiation. The product rule of derivatives states the following: $\dfrac{d}{dx}$(f(x)g(x)) = f(x) $\dfrac{d}{dx}$(g(x)) + g(x) $\dfrac{d}{dx}$(f(x)) …(I) Find the Derivative of xlogx Answer: … Read more
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