The nth derivative of 1/x is equal to (-1)nn!/xn+1. This is obtained by repeatedly using the power rule of differentiation. The nth derivative of 1/x is denoted by $\dfrac{d}{dx}\left( \dfrac{1}{x}\right)$, and its formula is given as follows: $\boxed{\dfrac{d}{dx}\left( \dfrac{1}{x}\right)=\dfrac{(-1)^n n!}{x^{n+1}}}$ nth Derivative of 1/x Question: How to find nth Derivative of 1/x? Answer: To find … Read more
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
The derivative of sin(xy) is equal to (y+x dy/dx) cos(xy), and this is the derivative of sin(xy) with respect to x. The derivative of sin(xy) formula is given below: $\dfrac{d}{dx}(\sin xy)=(y+x\dfrac{dy}{dx})\cos xy$. Differentiate sin(xy) with respect to x Answer: The derivative of sin(xy) with respect to x is equal to (y+x dy/dx) cos(xy). Explanation: Let … Read more
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 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 cot2x is equal to -2cosec22x. The differentiation of cot2x is denoted by d/dx (cot2x), and its formula is given by $\dfrac{d}{dx}$ (cot 2x) = -2cosec22x. cot2x Derivative Answer: The derivative of cot2x, that is, d/dx(cot2x) is equal to -2cosec22x. Explanation: To find the derivative of cot2x by the chain rule, let us … Read more
The derivative of ln4x is equal to 1/x. The derivative of ln4x is denoted by d/dx(ln4x), and its formula is given by $\dfrac{d}{dx}(\ln 4x)=\dfrac{1}{x}$. Find the Derivative of ln4x Answer: The derivative of ln(4x) is 1/x. Explanation: As ln4x = ln4 + lnx, the derivative of ln 4x is equal to $\dfrac{d}{dx}$ (ln 4x) = … Read more
The derivative of ln2x is 1/x, where ln denotes the natural logarithm. Here, the ln2x derivative is computed using the first principle and the chain rule of derivatives. Note that the derivative of ln2x is denoted by d/dx(ln2x), and its formula is given as follows: $\dfrac{d}{dx}(\ln 2x)=\dfrac{1}{x}.$ That is, the differentiation of ln2x is given … Read more
The derivative of lnx^2 is equal to 2/x. The natural logarithm of x2 is denoted by ln(x2), and its derivative formula is given by $\dfrac{d}{dx}(\ln x^2)=\dfrac{2}{x}.$ That is, the differentiation of ln(x2) is 2/x. Derivative of ln(x2) by Chain Rule Answer: The derivative of ln(x2) is 2/x. Explanation: To find the derivative of ln(x2) by … Read more
The derivative of lnx is equal to 1/x. Ln(x) denotes the natural logarithm of x, that is, lnx= logex. Here we will find the derivative of ln(x) using the limit definition and chain rule of differentiation. Note that lnx= logex. The derivative of lnx is denoted by d/dx(lnx), and its formula is given as follows: … Read more