Question

derivative sin(y)=x at point (0,pi)

Answer 1

-1

Answer 2

Derivative with respect to \(x\) or \(y\)?

I'll assume the former (w.r.t. \(x\)):
\[\begin{align*}\frac{d}{dx}\sin y&=\frac{d}{dx}x\\
\cos y\frac{dy}{dx}&=1\\
\frac{dy}{dx}=\sec y
\end{align*}\]
\(\bigg(\)If it indeed is w.r.t. \(y\), notice that \(\dfrac{dx}{dy}=\dfrac{1}{dy/dx}\), so \(\dfrac{dx}{dy}=\dfrac{1}{\sec y}=\cos y\bigg)\)

To find the derivative at a point \((x,y)\), you plug in the given \(x\) and \(y\). \(x=0\) and \(y=\pi\) in this case.