Consider the curve defined implicitly by

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

Problem

\sin(xy)+y=x^{2}

. The point

(0,0)

lies on this curve. (1) Calculate

\dfrac{dy}{dx}

in terms of

x

and

y

. (2) Determine the slope of the tangent line to the curve at the point

(0,0)