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Implicit Differentiation with Two Equations
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Implicit Differentiation with Two Equations
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Enter equations:
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| (2) |
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Obtain :
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Obtain :
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Stepwise Calculation:
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Replace with and
with :
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| (5) |
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Apply :
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![[2*__y__(__x__)*(diff(__y__(__x__), __x__))-2*__z__(__x__)-2*__x__*(diff(__z__(__x__), __x__)) = 0, 2*__x__+sin(__x__*__z__(__x__))*(__z__(__x__)+__x__*(diff(__z__(__x__), __x__))) = diff(__y__(__x__), __x__)]](/support/helpjp/helpview.aspx?si=3933/file05354/math136.png)
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Solve for both derivatives:
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![[diff(__y__(__x__), __x__) = -2*__x__/(sin(__x__*__z__(__x__))*__y__(__x__)-1), diff(__z__(__x__), __x__) = -(2*__y__(__x__)*__x__+__z__(__x__)*sin(__x__*__z__(__x__))*__y__(__x__)-__z__(__x__))/((sin(__x__*__z__(__x__))*__y__(__x__)-1)*__x__)]](/support/helpjp/helpview.aspx?si=3933/file05354/math148.png)
| (7) |
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Replace and with and , respectively:
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| (8) |
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