promath The exact solution of dy/dx=x+y is equal to |x+y+1| = Cex where C is a constant. In this post, we will learn how to solve the differential equation dy/dx =x+y. Solve dy/dx=x+y Question: Find the general solution of $\dfrac{dy}{dx}=x+y$. Solution: To solve the given differential equation, we will use the substitute method. Let us put … Read more
The simplification of cos3x -sin3x is equal to cos3x -sin3x = (cosx -sinx)(2+sin2x)/2. The formula of cos^3x +sin^3x is given as follows: cos3x +sin3x = $\dfrac{(\cos x +\sin x)(2-\sin 2x)}{2}$. Formula of cos3x -sin3x Prove that cos3x -sin3x = (cosx -sinx)(2+sin2x)/2. Solution: Applying the formula a3 -b3 = (a -b)(a2+ab+b2), we get that cos3x -sin3x … Read more
The partial derivative of xy with respect to x is equal to y and the partial derivative of xy with respect to y is equal to x. Their formula is given below: Partial Derivative of xy with respect to x Let us will find the partial derivative of xy using the definition. Let f(x, y) … Read more
The derivative of x/y with respect to x is equal to (-x dy/dx + y)/y2. Here, we will learn how to differentiate x/y with respect to x. Derivative of x/y with respect to x Question: Differentiate x/y with respect to x. Solution: Note that $\dfrac{x}{y}$ is a product of two functions $x$ and $\dfrac{1}{y}$. So … Read more
The derivative of the mod cosx is equal to (- sinx cosx)/|cosx|. Here let us learn how to differentiate mod cosx, that is, how to find d/dx(|cosx|). The derivative formula of mod cosx is given as follows. $\boxed{\dfrac{d}{dx}(|\cos x|)=\dfrac{-\sin x \cos x}{|\cos x|}}$, provided that cosx is non-zero. The following formula is very useful to … Read more
The integral of cosec square x is equal to -cot(x)+C where C is a constant. In this post, we will learn how to integrate cosec^2x. The integration formula of cosec^2x is given as follows: ∫cosec2x dx = -cotx+C What is the Integration of cosec^2x Answer: The integration of cosec2x is -cotx+C. Proof: First, recall the … Read more
The cot2x identity is given by cot2x = (cot2x-1)/2cotx. Note that cot2x is the cotangent of the angle 2x. The cot2x formula is as follows: cot2x = $\dfrac{\cot^2 x -1}{2 \cot x}$. Let us now learn how to prove the cot2x identity. Cot2x Formula in Terms of cotx The cot2x formula in terms of cotx … Read more
The cosec2x identity is given by cosec2x = (tanx + cotx)/2. That is, the formula of cosec 2x is equal to cosec 2x = $\dfrac{\tan x + \cot x}{2}$. Now, let us learn how to prove the cosec2x formula. Proof of cosec2x = (tanx+cotx)/2 Note that cosecx is the reciprocal of sinx. So we have … Read more
The value of sin(5pi/2) is equal to 1. The angle 5π/2 is equivalent to 450° and the value of sin 450° is equal to 1. The sin 5π/2 formula is given by $\sin \dfrac{5\pi}{2}=1.$ Let us learn how to find the value of sin(5pi/2). Value of Sin(5π/2) Answer: The value of sin 5π/2 is 1. … Read more
The value of cos(7pi/2) is equal to 0. Cos(7pi/2) is the value of cosine trigonometric function for 7π/2 radians. The formula of cos 7π/2 is given by $\boxed{\cos \dfrac{7\pi}{2} = 0}.$ Note that What is the Value of Cos 7pi/2? Answer: cos(7π/2) is equal to 0. Explanation: Note that 7π/2 can be written as follows. … Read more