promath The derivative of tan root x is equal to (sec2√x)/2√x. By the chain rule of differentiation, the derivative formula of tan(√x) with respect to x is given as follows: $\dfrac{d}{dx}(\tan \sqrt{x})=\dfrac{\sec^2 \sqrt{x}}{2\sqrt{x}}$. Derivative of tan(√x) by Chain Rule Answer: The derivative of tan√x is (sec2√x)/2√x. Explanation: Let us put z = √x. Differentiating both sides … Read more
The derivative of cos root x is equal to (-sin√x)/2√x. Here we will find the derivative of cos√x by the chain rule of derivatives. The differentiation of cos(√x) with respect to x is given by $\dfrac{d}{dx}(\cos \sqrt{x})=-\dfrac{\sin \sqrt{x}}{2\sqrt{x}}$. Let us now find the derivative of cos root x using the chain rule of differentiation. Derivative … Read more
The general solution of the differential equation dy/dx = xy2 is given by y=-2/(x2+2K) where K is an arbitrary constant. Here we will learn how to find the general solution of the differential equation. Set C=2K. Answer: the solution of $\dfrac{dy}{dx}=xy^2$ is given by y = $-\dfrac{2}{x^2+C}$. Solve dy/dx=xy2 Given $\dfrac{dy}{dx}=xy^2$ To solve it, we … Read more
The 1-sinx formula is given by 1-sinx= [cos(x/2) -sin(x/2)]2. The 1 plus sinx idenity is given as follows: $1+\sin x =(\cos \frac{x}{2}+\sin \frac{x}{2})^2$. Let us now find the formula of 1-sinx and 1+sinx. Formula of 1-sinx Answer: 1-sinx= $(\cos \frac{x}{2}-\sin \frac{x}{2})^2$. Explanation: To find the formula of 1-sinx, we will use the following two trigonometric … Read more
The 1-cosx identity is given by 1-cosx= 2sin2(x/2). 1 minus cosx is a trigonometric expression and its formula is given below: $1-\cos x =2 \sin^2 (\frac{x}{2})$. Let us now find the formula of 1-cosx in terms of sin. 1-cosx Formula in Terms of Sin Answer: 1-cosx formula in terms of sin is equal to 1-cosx= … Read more
Cot(a+b) Cot(a-b) can be expressed in terms of cot as well as tan. In this post, we will learn to find cot(a+b)cot(a-b) formula with proof. Let us now find the formula of the product cot(a+b) and cot(a-b). Cot(a+b) Cot(a-b) Formula in Terms of Cot Using the identities of cot(a+b) and cot(a-b), the given expression can … Read more
The value of sin18° is equal to (√5-1)/4 and the value of cos18° is equal to √(10+2√5)/2. Here we will learn to find the values of sin18, cos18. The sin 18 degree formula is given by $\boxed{\sin 18^\circ = \dfrac{\sqrt{5}-1}{2}}$ The cos 18 degree formula is given by $\boxed{\cos 18^\circ = \dfrac{\sqrt{10+2\sqrt{5}}}{2} }$ Value of … Read more
The value of sin(3pi/4) is equal to 1/√2. As the angle 3π/4 is same as 135° in degrees, the value of sin135° is 1/√2. The sin 3π/4 formula is given as follows $\boxed{\sin \dfrac{3\pi}{4}=\dfrac{1}{\sqrt{2}} }$ Let us learn how to find the value of sin(3pi/4). Value of Sin(3π/4) Answer: The value of sin 3π/4 is … Read more
Let us talk about how to use ChatGPT for maths. Students are often curious to know how to solve Math using ChatGPT. As we all know ChatGPT is a very powerful artificial intelligence (AI) tool now a days to solve many problems, such as, writing codes in different computer languages, blog articles, making tour plans, … Read more
The derivative of sinx/(1+cosx) [sinx divided by 1+cosx] is equal to 1/(1+cosx), and it is denoted by d/dx (sinx/1+cosx). That is, $\dfrac{d}{dx} \big(\dfrac{\sin x}{1+\cos x} \big)=\dfrac{1}{1+\cos x}$. Here we will learn how to differentiate sinx divided by 1+cosx. Differentiate sinx/(1+cosx) Question: If y= sinx/1+cosx, then find dy/dx. Answer: If y=sinx/(1+cosx), then dy/dx = 1/(1+cosx). Explanation: … Read more