If 74+5f(x)+8x2(f(x))3=0 and f(−1)=−2 , find f′(−1) .

Answer 1

74+5f(x)+8x²f³(x)=0

Take the derivative empirically.

0+5f '(x)+24x²f²(x)f '(x)+16xf³(x)=0

f '(x)(5+24x²f²(x)) = -16xf³(x)

f '(x) = -16xf³(x)/(5+24x²f²(x))

f '(-1) = -16(-1)(-2)³/(5+24(-1)²(-2)²)

I'll let you finish the arithmetic