Let f(x) \( x^n+ax^{n-1}+a^2x^{n-2}+....+a^{n-1}x+a^n\)
\( \dfrac{d}{dx}f(x)= ( x^n+ax^{n-1}+a^2x^{n-2}+....+a^{n-1}x+a^n)\)
\( \dfrac{d}{dx}(x^n)+a\dfrac{d}{dx}(x^{n-1})+a^2+\dfrac{d}{dx}(x^{n-2})\)
\( +....+a^{n-1}\dfrac{d}{dx}(x)+a^n\dfrac{d}{dx}(1)\)
On using theorem \( \dfrac{d}{dx}(x^n)=nx^{n-1}\) we obtain
\( f'(x)=nx^{n-1}+a(n-1)x^{n-2}+a^2(n-2)x^{n-3}\)
\( +...+a^{n-1}+a^n(0)\)
\( f'(x)=nx^{n-1}+a(n-1)x^{n-2}+a^2(n-2)x^{n-3}\)
\( +...+a^{n-1}+a^n\)
Answered by Abhisek | 1 year ago