frac{d^n}{dx^n}(log x) = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $y = \log x$. First derivative: $y_1 = \frac{d}{dx}(\log x) = \frac{1}{x} = x^{-1}$. Second derivative: $y_2 = \frac{d}{dx}(x^{-1}) = -1 \cdot

Vedclass · Accepted Answer

$\frac{(-1)^{n - 1}(n - 1)!}{x^n}$

Vedclass · Answer

(D) Let $y = \log x$. First derivative: $y_1 = \frac{d}{dx}(\log x) = \frac{1}{x} = x^{-1}$. Second derivative: $y_2 = \frac{d}{dx}(x^{-1}) = -1 \cdot x^{-2} = \frac{-1}{x^2}$. Third derivative: $y_3 = \frac{d}{dx}(-x^{-2}) = -1 \cdot (-2) \cdot x^{-3} = \frac{2}{x^3} = \frac{2!}{x^3}$. Fourth derivative: $y_4 = \frac{d}{dx}(2x^{-3}) = 2 \cdot (-3) \cdot x^{-4} = \frac{-6}{x^4} = \frac{-3!}{x^4}$. By observing the pattern,the $n^{th}$ derivative is given by: $y_n = \frac{(-1)^{n-1}(n-1)!}{x^n}$.

$\frac{d^n}{dx^n}(\log x) =$

Similar Questions

If $y = \cos^2\left(\frac{5x}{2}\right) - \sin^2\left(\frac{5x}{2}\right)$,then $\frac{d^2y}{dx^2} =$

If $y = \sin(m \sin^{-1} x)$,then $(1-x^2) y_2 - x y_1$ is equal to (Here,$y_n$ denotes $\frac{d^n y}{dx^n}$)

If $f(x) = 10 \cos x + (13 + 2x) \sin x$,then $f''(x) + f(x)$ is equal to

$f(x) = e^x \sin x$,then $f^{(6)}(x)$ is equal to :

If $y=ax^{n+1}+b x^{-n}$,then $x^2 \frac{d^2 y}{d x^2}=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module