Question

Find dy/dx by implicit differentiation and evaluate the derivative at the given point.

Answer 1

$\tan(5x+y)=5x$

Differentiating both sides yields

$\sec^2(5x+y)\times\left(5+\dfrac{\mathrm dy}{\mathrm dx}\right)=5$
$\dfrac{\mathrm dy}{\mathrm dx}=5\cos^2(5x+y)-5$

At the point (0,0), you get

$\dfrac{\mathrm dy}{\mathrm dx}=5\cos^2(5(0)+0)-5=5-5=0$