The curve given by passes through the point .

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

The curve given by

x^{2}y+y^{3}=4

passes through the point

(1,1)

. (1) Find an explicit expression for

\dfrac{dy}{dx}

in terms of

x

and

y

. Simplify completely. (2) Evaluate

\dfrac{dy}{dx}

at the point

(1,1)

. (3) Determine the equation of the normal line to the curve at

(1,1)