promath The integration of root tanx + root cotx is equal to √2sin-1(sinx−cosx)+C. Here we learn how to integrate √tanx+√cotx. The integral formula of $\sqrt{\tan x}+\sqrt{\cot x}$ is given by $\int (\sqrt{\tan x}+\sqrt{\cot x}) dx$ = $\sqrt{2}\sin^{-1}(\sin x -\cos x)+C$. Find ∫(√tanx+√cotx) dx $\int (\sqrt{\tan x}+\sqrt{\cot x}) dx$ = $\int \Big(\dfrac{\sqrt{\sin x}}{\sqrt{\cos x}}+\dfrac{\sqrt{\cos x}}{\sqrt{\sin x}} \Big) … Read more
The derivative of ln(lnx) is equal to 1/xln(x) and it is denoted by d/dx (x lnx). So the derivative formula of ln(lnx) is given by $\dfrac{d}{dx}\big(\ln(\ln x) \big) = \dfrac{1}{x \ln x}$. Derivative of ln(lnx) by Chain Rule Answer: The derivative of ln(lnx) is $\dfrac{1}{x \ln x}$. Explanation: Let z=ln x. Differentiating, $\dfrac{dz}{dx}=\dfrac{1}{x}$. Now, $\dfrac{d}{dx}\big(\ln(\ln … Read more
The derivative of 4/x is equal to -4/x2. In this post, we will find the derivative of 4 divided by x by the power rule. The derivative of 4/x is denoted by d/dx(4/x), and its formula is given by $\dfrac{d}{dx}(\dfrac{4}{x})= – \dfrac{4}{x^2}$. Derivative of 4/x Question: Find the Derivative of 4/x. Answer: We can express … Read more
The derivative of 3/x is equal to -3/x2. The derivative formula of 3/x (3 divided by x) is given by as follows: $\dfrac{d}{dx}(\dfrac{3}{x})= – \dfrac{3}{x^2}$. Derivative of 3/x Question: What is the Derivative of 3/x? Answer: As 3/x can be expressed as 3x-1, applying the power rule, the derivative of 3/x is equal to -3/x². … Read more
The derivative of 2/x is equal to -2/x2. Here, we will learn how to find the derivative of 2 divided by x. The derivative formula of 2/x is given by $\dfrac{d}{dx}(\dfrac{2}{x})= – \dfrac{2}{x^2}$. Derivative of 2/x Question: Find the Derivative of 2/x. Answer: We can express 2/x as 2x-1. So by the power rule, the … Read more
The integral of $\sqrt{1-x^2}$ is equal to $\dfrac{x}{2} \sqrt{1-x^2}$ $+\dfrac{1}{2}$ sin-1 x+C. Here we will learn how to integrate square root of 1-x2. The integral formula of root 1-x^2 is provided below:$\int \sqrt{1-x^2} dx$ $=\dfrac{x}{2} \sqrt{1-x^2}$ $+\dfrac{1}{2}$ sin-1 x+C. Integration of $\sqrt{1-x^2}$ Question: How to Integrate Root (1-x^2)? That is, find $\int \sqrt{1-x^2} dx$. Solution: … Read more
The integral of root tanx is equal to ∫√tanx dx = $\dfrac{1}{\sqrt{2}}$ tan-1 ($\dfrac{\tan x-1}{\sqrt{2\tan x}}$) + $\dfrac{1}{2\sqrt{2}}$ log $|\dfrac{\tan x+1-\sqrt{2\tan x}}{\tan x+1+\sqrt{2\tan x}}|$ +C where C denotes an integral constant. In this post, we will learn how to find the integral of square root of tanx. Integration of √tanx Question: Find ∫√tanx dx. Solution: … Read more
The derivative of ln(1/x) is equal to -1/x, where ln denotes the logarithm with base e, that is, ln(x)=logex. In this post, we will find the derivative of ln(1/x). Note that ln(1/x) is the natural logarithm of 1/x. Its derivative formula is given below: $\dfrac{d}{dx}\big( \ln (\dfrac{1}{x}) \big)=-\dfrac{1}{x}$. Derivative of ln(1/x) by Chain Rule Let … Read more
The derivative of root 1-x^2 is equal to -x/√(1-x2). Here we differentiate square root of 1-x2 by chain rule and implicit differentiation method. Note that $\dfrac{d}{dx} \Big( \sqrt{1-x^2}\Big)=-\dfrac{x}{\sqrt{1-x^2}}$. Let us now differentiate root 1-x2. Derivative of root 1-x2 by Chain Rule Question: Find the derivative of square root 1-x2. Answer: Let us put z = … Read more
The Laplace transform of delta function is equal to L{δ(t)} = 1. Here we find the Laplace of Dirac delta function, that is, unit impulse function. The Dirac delta function is also known as the unit impulse function. Its Laplace transform formula is given by L{δ(t)} = 1. Laplace Transform of Dirac Delta Function Recall … Read more