Roots Again...

P(x)=(x-t_{1})(x-t_{2})..............(x-t_{n})
\frac{P(x)}{(x-t_{1})}=(x-t_{2})..............(x-t_{n})\lim_{x\rightarrow t_{1}}\frac{P(x)}{(x-t_{1})}=(t_{1}-t_{2})(t_{1}-t_{3})..............(t_{1}-t_{n})
applying l'hospital's rule
\lim_{x\rightarrow t_{1}}\frac{P'(x)}{(1)}=(t_{1}-t_{2})(t_{1}-t_{3})..............(t_{1}-t_{n})
\frac{P'(t)}{(1)}=(t_{1}-t_{2})(t_{1}-t_{3})..............(t_{1}-t_{n})
hence asnswer is :
nt₁^n-1+p

Yup done...!

Guess what, i took d/dx(xⁿ)= nxⁿ while solving in the test [16]....khair chodo ab kya kar sakte hain....thnx karna