[tex]\tan(5x+y)=5x[/tex]
Differentiating both sides yields
[tex]\sec^2(5x+y)\times\left(5+\dfrac{\mathrm dy}{\mathrm dx}\right)=5[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=5\cos^2(5x+y)-5[/tex]
At the point (0,0), you get
[tex]\dfrac{\mathrm dy}{\mathrm dx}=5\cos^2(5(0)+0)-5=5-5=0[/tex]
