+118723 If f(x)+x^5[f(x)]^3=2052 and f(2)=4, find f′(2)
\(f(x)+x^5[f(x)]^3=2052\qquad f(2)=4,\qquad find f′(2)\\ f'(x)+x^5*3[f(x)]^2*f'(x)+5x^4*[f(x)]^3=0\\ f'(2)+2^5*3[f(2)]^2*f'(2)+5*2^4*[f(2)]^3=0\\ f'(2)+32*3[4]^2*f'(2)+5*16*[4]^3=0\\ f'(2)+32*3*16*f'(2)+5*16*64=0\\ f'(2)+1536*f'(2)+5120=0\\ 1537*f'(2)=-5120\\ f'(2)=\frac{-5120}{1537}\\ \)
