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 $f(x)$ and $g(x)$ are twice differentiable functions on $(0,3)$ satisfying $f^{\prime \prime}(x)=g^{\prime \prime}(x)$, $f^{\prime}(1)=4$, $g^{\prime}(1)=6$, $f(2)=3$, and $g(2)=9$, then $f(1)-g(1)$ is

If $y=a \cos (\sin 2 x)+b \sin (\sin 2 x)$, then $y^{\prime \prime}+(2 \tan 2 x) y^{\prime}$ is equal to

If $y = \frac{\sinh^{-1} x}{\sqrt{1+x^2}}$,then $(1+x^2) y_2 + 3xy_1 + y = $

If $y = \log(\cosh x)$,then $\frac{d^2 y}{d x^2} = $

If $f(x) = \sin(\sin x)$ and $f''(x) + \tan x f'(x) + g(x) = 0$,then $g(x)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module