Jika z = 4x² – 2y²; x = 3s + 5t dan y = 3st; carilah dz/dt
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Jawaban:
[tex] \frac{dz}{dt} = 120s + 200t - 36 {s}^{2} t[/tex]
Penjelasan dengan langkah-langkah:
[tex] \frac{dz}{dt} = (\frac{dz}{dx} \times \frac{dx}{dt} ) + (\frac{dz}{dy} \times \frac{dy}{dt} )[/tex]
[tex] \frac{dz}{dt} = ((8x) \times (5)) + (( - 4y) \times (3s))[/tex]
[tex] \frac{dz}{dt} = 40x - 12ys[/tex]
[tex] \frac{dz}{dt} = 40(3s + 5t) - 12(3st)s[/tex]
[tex] \frac{dz}{dt} = 120s + 200t - 36 {s}^{2} t[/tex]
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