When differentiating implicitly, what is \(d(y)/dx\)?

What is \(d(y^2)/dx\) when \(y\) depends on \(x\)?

Differentiate \(x^2+y^2=25\) implicitly.

Differentiate \(xy=6\) implicitly and solve for \(dy/dx\).

Find \(dy/dx\) for \(x^2+3y=10\).

Find \(dy/dx\) for \(y^3+x=4\).

Find \(dy/dx\) for \(x^2+xy+y^2=7\).

Find \(dy/dx\) for \(x^3+y^3=9xy\).

For \(x^2+y^2=25\), find the slope at \((3,4)\).

Find \(dy/dx\) for \(\sin y=x\).

Find \(dy/dx\) for \(e^y+x^2=5\).

For \(x^2+xy+y^2=3\), find the slope at \((1,1)\).

Find \(dy/dx\) for \(\frac{x^2}{4}+\frac{y^2}{9}=1\).

Find \(dy/dx\) for \(\ln y=x^2\), stating the condition on \(y\).

Find \(dy/dx\) for \(x\sin y=y\cos x\).

For \(x^2+y^2=r^2\), find the tangent slope and explain why it is undefined at \((r,0)\).

Find \(d^2y/dx^2\) for \(x^2+y^2=25\) in terms of \(x\) and \(y\).

A student differentiates \(y^2\) as \(2y\). Explain the mistake in implicit differentiation.

For \(x^2+xy+y^2=3\), find points on the curve where the tangent is horizontal.

Show that the ellipse \(x^2/a^2+y^2/b^2=1\) has slope \(-b^2x/(a^2y)\).