promath 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
The derivative of arc(cotx) is equal to -1/(1+x2). In this post, we will learn how to differentiate cot inverse x. The derivative formula of cot-1x is given by d/dx (cot-1x) = -1/(1+x2). What is the derivative of arc cotx? Answer: The derivative of arccotx is -1/(1+x2). Solution: Let y = arc cotx …(∗) As we … Read more
The derivative of root tanx is equal to sec2x/(2√tanx). In this post, we will learn how to differentiate the square root of tan x using the first principles. Derivative of square root of tanx from first principle Question: Find the derivative of $\sqrt{\tan x}$ from first principle. Solution: The below steps have to be followed … Read more
The derivative of root cosx is equal to -sinx/(2√cosx). In this post, we will learn how to differentiate the square root of cos x by the chain rule of derivatives. Derivative of Square Root of cos x by Chain Rule Question: Find the derivative of $\sqrt{\cos x}$ by the chain rule. Solution: To find the … Read more
The derivative of root sinx is equal to cosx/(2√sinx). In this post, we will learn how to differentiate square root of sinx by the chain rule of derivatives. Derivative of Square Root of Sin x by Chain Rule Question: Find the Derivative of $\sqrt{\sin x}$ by the chain rule. Solution: To find the derivative of … Read more
The limit of sinx/x as x approaches infinity is equal to zero. That is, limx→∞ sinx/x = 0. This can be proved using the Squeeze Theorem of limits which will be done here. Limit of sinx/x as x goes to infinity Question: What is the limit of sinx/x when x→∞. Answer: The limit of sinx/x … Read more
The derivative of 1/cos is equal to secx tanx. In this post, we will learn how to differentiate 1 over cosx with respect to x. What is the Derivative of 1/cosx? Answer: The derivative of 1/cosx with respect to x is denoted by d/dx(1/cosx) and it is given below. $\dfrac{d}{dx}(\dfrac{1}{\cos x})$ = $\sec x \tan … Read more
The derivative of 1/sinx is equal to -cosecx cotx. In this post, we will learn how to differentiate 1 by sinx with respect to x. What is the Derivative of 1/sinx? Answer: The derivative of 1/sinx with respect to x is denoted by d/dx(1/sinx) and it is equal to -cosec(x)cot(x). That is, $\dfrac{d}{dx}(\dfrac{1}{\sin x})$ = … Read more