## Partial Derivative of log(x^2+y^2): Formula, Proof

The partial derivative of log(x^2+y^2) with respect to x is equal to 2x/(x2+y2) and with respect to y is equal to 2y/(x2+y2). So their formulas are as follows: Function Partial Derivative z=log(x2+y2) ∂z/∂x = 2x/(x2+y2) z=log(x2+y2) ∂z/∂y = 2y/(x2+y2) where ∂z/∂x is the partial derivative of z with respect to x. Partial Derivative of log(x2+y2) … Read more

## If y=cos(x+y) then Find dy/dx [Solved]

If y=cos(x+y), then dy/dx= -sin(x+y)/[1+sin(x+y)]. Here, we learn how to differentiate y=cos(x+y) with respect to x. Let us find the derivative of y=cos(x+y). Find dy/dx if y=cos(x+y) Question: If y=cos(x+y), then $\dfrac{dy}{dx}$. Solution: We are given that y = cos(x+y). Step 1: Differentiating both sides of the above equation with respect x, we get that … Read more

## If y=sin(x+y) then Find dy/dx [Solved]

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

## Derivative of ln(x+1): Proof by First Principle, Chain Rule

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

## Derivative of x^10: Proof by First Principle, Power Rule

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

## Partial Derivative of xy [With Respect to x and y]

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

## Derivative of root tanx by First Principle

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

## Derivative of root cosx by Chain Rule

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

## Derivative of root sinx by Chain Rule

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

## Limit of (e^x-1)/x as x approaches 0: Formula, Proof

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