mckinneya14
mckinneya14 mckinneya14
  • 22-02-2017
  • Mathematics
contestada

Find dy/dx by implicit differentiation and evaluate the derivative at the given point.
tan(5x + y) = 5x, (0, 0)

Respuesta :

LammettHash
LammettHash LammettHash
  • 25-02-2017
[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]
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