promath 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
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