If y=sin(x+y), then dy/dx= cos(x+y)/[1-cos(x+y)]. Here, we learn how to differentiate y=sin(x+y) with respect to x. Let us find the derivative of y=sin(x+y). y=sin(x+y), Find dy/dx Question: If y=sin(x+y), then $\dfrac{dy}{dx}$. Solution: Given, y = sin(x+y). To find dy/dx, we will differentiate both sides of the equation y=sin(x+y) with respect x. Using the chain rule, … Read more
The derivative of ln(x+1) is equal to 1/(x+1). Ln(x+1) denotes the natural logarithm of x+1, that is, ln(x+1) = loge(x+1). Here we will find the derivative of ln(x+1) using the following methods: The derivative of ln(x+1) is denoted by d/dx {ln(x+1)} and its formula is given by $\dfrac{d}{dx} \Big(\ln (x+1) \Big)=\dfrac{1}{x+1}.$ Derivative of ln(x+1) by … Read more
The derivative of x^10 (x to the power 10) is 10×9. In this post, we will find the derivative of x10 by the first principle and the power rule of derivatives. The derivative of x10 is denoted by d/dx (x10), and its formula is given by $\dfrac{d}{dx}(x^{10})=10x^9$. Derivative of x^10 by First Principle The derivative … Read more
The partial derivative of xy with respect to x is equal to y and the partial derivative of xy with respect to y is equal to x. Their formula is given below: Partial Derivative of xy with respect to x Let us will find the partial derivative of xy using the definition. Let f(x, y) … 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 (ex-1)/x, when x tends to zero, is equal to 1. That is, the formula of the limx→0 (ex-1)/x is given by limx→0 (ex-1)/x = 1. In this post, we will learn to find the limit of the function (ex-1)/x when x approaches to zero. Limit of (e^x-1)/x as x→0 Prove that limx→0 … 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