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Lera25 [3.4K]
3 years ago
12

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

Mathematics
1 answer:
LekaFEV [45]3 years ago
3 0
\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
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