Find dy/dx for the following function and evaluate the derivative at the point (2, -1). x 2 + y 2 x = − 2

Question

Find dy/dx for the following function and evaluate the derivative at the point (2, -1).      x          2        +      y          2        x  =  −  2

Hamza Conrad · Accepted Answer

x          2        +      y          2        x  =  −  2  2  x  +      y          2        +  2  x  y            d      y              d      x        =  0  2  ∗  2  +  (  −  1      )          2        +  2  ∗  2  ∗  −  1            d      y              d      x        =  0  4  +  1  −  4            d      y              d      x        =  0  ⇒            d      y              d      x        =      5    4  equation line:   y  +  1  =      5    4    (  x  −  2  )4y+4=5x-104y=5x-14

Taliyah Reyes · Accepted Answer

Use implicit differentation      d          d      x        (      x          2        )  +      d          d      x        (      y          2        x  )  =      d          d      x        (  −  2  )Use the power rule and the product rule  2  x  +      y          2            d          d      x        (  x  )  +  x      d          d      x        (      y          2        )  =  0  2  x  +      y          2        +  x      d          d      x        (      y          2        )  =  0Use the chain rule  2  x  +      y          2        +  2  x  y            d      y              d      x        =  0Solve for dy/dx            d      y              d      x        =            −      2      x      −              y                  2                            2      x      y      Now evaluate at (2, -1).            d      y              d      x        =            −      2      (      2      )      −      (      −      1              )                  2                            2      (      2      )      (      −      1      )                  d      y              d      x        =            −      4      −      1              −      4        =            −      5              −      4        =      5    4

Find dy/dx for the following function and evaluate the derivative at the point (2, -1). x^2+y^2 x=-2

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