KCET · Maths · Functions
If the function \( g(x) \) is defined by
\[
g(x)=\frac{\chi^{200}}{200}+\frac{\chi^{199}}{199}+\frac{\chi^{198}}{198}+\ldots \ldots+\frac{\chi^{2}}{2}+\chi+5, \text { then } g^{\prime}(0)=
\]
- A \( 11 \)
- B \( 200 \)
- C \( 100 \)
- D \( 55 \)
Answer & Solution
Correct Answer
(A) \( 11 \)
Step-by-step Solution
Detailed explanation
Given that,
\[
\begin{array}{l}
g(x)=\frac{\chi^{200}}{200}+\frac{\chi^{199}}{199}+\frac{\chi^{198}}{198}+\cdot s+\frac{\chi^{2}}{2}+\chi+5 \\
\text { So, } g^{\prime}(x)=\frac{200 x^{199}}{200}+\frac{199 x^{198}}{199}+s+\frac{2 x}{2}+1+0
\end{array}
\]
At \( x=0 \), we have \( g^{\prime}(0)=1 \)
\[
\begin{array}{l}
g(x)=\frac{\chi^{200}}{200}+\frac{\chi^{199}}{199}+\frac{\chi^{198}}{198}+\cdot s+\frac{\chi^{2}}{2}+\chi+5 \\
\text { So, } g^{\prime}(x)=\frac{200 x^{199}}{200}+\frac{199 x^{198}}{199}+s+\frac{2 x}{2}+1+0
\end{array}
\]
At \( x=0 \), we have \( g^{\prime}(0)=1 \)
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