Question

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

tan(5x + y) = 5x, (0, 0)

Answer 1

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

Differentiating both sides yields


`\sec^2(5x+y)*\left(5+(\mathrm dy)/(\mathrm dx)\right)=5`

`(\mathrm dy)/(\mathrm dx)=5\cos^2(5x+y)-5`

At the point (0,0), you get


`(\mathrm dy)/(\mathrm dx)=5\cos^2(5(0)+0)-5=5-5=0`