promath The general solution of the differential equation dy/dx=x/y is given by y2 = x2 + C where C is an integral constant. Here we will learn how to find the solution of dy/dx=x/y. General Solution of dy/dx=x/y Question: Find the general solution of dy/dx=x/y. Answer: The given differential equation is $\dfrac{dy}{dx}=\dfrac{x}{y}$ Separating the variables x … Read more
The derivative of 1/x is equal to -1/x2. In this blog post, we will learn how to find the differentiation of 1/x. Derivative of 1/x Formula: The formula of the derivative of 1/x is given by d/dx(1/x) = -1/x2. Let us find the differentiation of 1/x by first principle which is equal to -1/x2. Derivative … Read more
The derivative of fifth root of x is 1/(5×4/5). In this post, we will learn how to find the derivative of the fifth root x. Here, we will use the power rule of derivatives. Note that the fifth root of x can be written as $\sqrt[5]{x}$ Or, following the rule of indices, the fifth root … Read more
The derivative of 1/lnx is equal to -1/x(lnx)2. In this post, we will learn how to differentiate 1 divided by lnx with respect to x. Let us now find the derivative of 1/lnx using the chain rule and the power rule of derivatives. What is the Derivative of 1/lnx? Answer: The derivative of 1/lnx with … Read more
The derivative of square root of 2x is equal to 1/√(2x). In this post, we will learn how to find the derivative of the square root of 2x. The derivative of the square root of 2x is given by the following formula: $\dfrac{d}{dx}(\sqrt{2x})$ = $\dfrac{1}{\sqrt{2x}}$ Derivative of root 2x by Power Rule To find the … Read more
The derivative of 1/2x is equal to -1/2×2. In this post, we will learn how to find the derivative of 1 divided by 2x. The derivative formula of 1/2x is given by $\dfrac{d}{dx}(\dfrac{1}{2x})= – \dfrac{1}{2x^2}$. Derivative of 1/2x by Power Rule Let us find the derivative of 1 by 2x by the power rule of … Read more
The derivative of root 3x is equal to √3/(2√x). In this post, we will learn how to find the derivative of the square root of 3x. Now, we find the derivative of square root of 3x by the power rule. Derivative of root 3x by Power Rule Let us find the derivative of square root … Read more
The integration of x/(1+x), that is, the integral of x divided by 1+x is equal to x – ln|1+x|+C. In this post, we will learn how to integrate x/(1+x). To find the integral $\int \dfrac{x}{1+x} dx$, we will use the following power rule of the integration formula: ∫dx/x =ln|x|+C …(I) Integration of x/(1+x) Question: Find … Read more
The integration of x/(1+x^2), that is, the integral of x divided by 1+x2 is equal to 1/2 ln(1+x2) + C, where C is a constant. Here ln denotes the natural logarithm. In this post, we will learn how to integrate x divided by 1+x^2. Let’s find the integral: $\int \dfrac{x}{1+x^2} dx$. To find the above … Read more
Note that arc(cotx) is an inverse trigonometric function. We will find the derivative of arc(cotx) and it is equal to -1/(1+x2). In this post, we will learn how to differentiate the function arc cotx. What is the derivative of arc cotx? Answer: The derivative of arccotx is -1/(1+x2). Solution: [Method 1]: Let y = arc … Read more