(x) + x^{2}**[**f(x)**]**^{3} = 10

f(1) = 2 (when x=1 , f(x)=2)

2 + 1^{2}(2)^{3 }= 10

2 + 8 = 10

10 = 10

Evaluate the derivative of f(x) using the point (1, 2)

Let f(x) = y

y + x^{2}y^{3} = 10

Derive both sides

y' + 2xy^{3} + 3x^{2}y^{2}y' = 0

y' + 3x^{2}y^{2}y' = -2xy^{3}

y' (1 + 3x^{2}y^{2}) = -2xy^{3}

f'(x) = (-2xy^{3}) / (1 + 3x^{2}y^{2})

So what is f'(x) at x=1.

f'(1) = **(**-2(2^{3})**)** / **(**1 + 3(2^{2})**)**

f'(1) = -16 / (1 + 12)

f'(1) = -16 / 13