If the function g(x) is defined by g(x) = fra | vedclass

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

Question

(B) Given the function: $g(x) = \frac{x^{200}}{200} + \frac{x^{199}}{199} + \dots + \frac{x^2}{2} + x + 5$. To find $g'(x)$,we differentiate $g(x)$ wi

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) Given the function: $g(x) = \frac{x^{200}}{200} + \frac{x^{199}}{199} + \dots + \frac{x^2}{2} + x + 5$. To find $g'(x)$,we differentiate $g(x)$ with respect to $x$ using the power rule $\frac{d}{dx}(x^n) = nx^{n-1}$: $g'(x) = \frac{200x^{199}}{200} + \frac{199x^{198}}{199} + \dots + \frac{2x}{2} + 1 + 0$. Simplifying the expression,we get: $g'(x) = x^{199} + x^{198} + \dots + x + 1$. Now,substitute $x = 0$ into the derivative: $g'(0) = 0^{199} + 0^{198} + \dots + 0 + 1$. $g'(0) = 1$.

If the function $g(x)$ is defined by $g(x) = \frac{x^{200}}{200} + \frac{x^{199}}{199} + \frac{x^{198}}{198} + \dots + \frac{x^2}{2} + x + 5$,then find $g'(0)$.

Similar Questions

Let $h(x) = \frac{5(f(x))^3}{3} + \frac{(f(x))^2}{2} + 2f(x) + 100$,where $f(x)$ is a differentiable function. Then which one of the following is correct?

Let $F(x)=e^{x}$, $G(x)=e^{-x}$ and $H(x)=G(F(x))$, where $x$ is a real variable. Then, $\frac{dH}{dx}$ at $x=0$ is

If $f(2)=4$ and $f^{\prime}(2)=1$,then $\lim _{x \rightarrow 2} \frac{x f(2)-2 f(x)}{x-2}$ is equal to

If $[x]$ represents the greatest integer function and $f(x) = x - [x] - \cos x$,then $f^{\prime}\left(\frac{\pi}{2}\right) = $

If $y = f \left( \frac{2x - 1}{x^2 + 1} \right)$ and $f'(x) = \sin x$,then $\frac{dy}{dx} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module