Answer: The derivative of x^2 sin(1/x) at x=0 is equal to 0 if the function is defined to be 0 at x=0. Question Find the derivative of the function f(x) = $\begin{cases} x^2 \sin(\frac{1}{x}) & \text{if } x \neq 0 \\ 0 & \text{if } x=0 \end{cases}$ at x=0. That is, find f'(0). Solution From … Read more
The derivative of ln(ln(x)) is equal to 1/{x lnx ln(lnx)}. This is obtained by using the chain rule of differentiation. In this post, lets learn how to differentiate ln(ln(lnx)). Differentiation of ln(ln(lnx)) Step 1: Recall, the chain rule of differentiation: Suppose $f$ is a function of $z$ and $z$ is a function of $x$, that … Read more
The nth derivative of cosx is equal to cos(nπ/2 +x). The nth derivative of cos x is denoted by dn/dxn (cosx), and its formula is given as follows: $\boxed{\dfrac{d^n}{dx^n}\left( \cos x\right)=\cos \left(\dfrac{n \pi}{2}+x \right)}$ nth Derivative of cos x Question: Find the nth derivative of cosx. Answer: To find the nth derivative of cosx with … Read more
The nth derivative of sinx is equal to sin(nπ/2 +x). The nth derivative of sin x is denoted by dn/dxn (sinx), and its formula is given as follows: $\boxed{\dfrac{d^n}{dx^n}\left( \sin x\right)=\sin \left(\dfrac{n \pi}{2}+x \right)}$ nth Derivative of sin x Question: Find the nth Derivative of sinx. Answer: To find the nth derivative of sinx with … Read more
The nth derivative of 1/(ax+b) is equal to (-1)nn!an/(ax+b)n+1. The nth derivative of 1/(ax+b) is denoted by $\dfrac{d^n}{dx^n}\left( \dfrac{1}{ax+b}\right)$ and its formula is given below: $\boxed{\dfrac{d^n}{dx^n}\left( \dfrac{1}{ax+b}\right)=\dfrac{(-1)^n n! a^n}{(ax+b)^{n+1}}}$ nth Derivative of 1/(ax+b) Question: What is the nth Derivative of $\dfrac{1}{ax+b}$? Answer: Let us put y = $\dfrac{1}{x+b}$ = (ax+b)-1. Using the power rule $\dfrac{d}{dx}\left( … Read more
The nth derivative of xn is equal to n!. The nth derivative of x^n is denoted by $\frac{d^n}{dx^n}\left( x^n\right)$, and its formula is given as follows: $\boxed{\dfrac{d^n}{dx^n}\left( x^n\right)=n!}$ nth Derivative of xn Question: Find nth Derivative of xn. Answer: The nth derivative of x to the power n is obtained by repeatedly using the power … Read more
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 $\dfrac{d^n}{dx^n}\left( \dfrac{1}{x}\right)$, and its formula is given as follows: $\boxed{\dfrac{d^n}{dx^n}\left( \dfrac{1}{x}\right)=\dfrac{(-1)^n n!}{x^{n+1}}}$ 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