1. Find the indicated partial derivatives. Use product, quotient, and chain rule as needed. a) f(x,y) = ?(5x² + x²y - 3y²), fy b) f(x,y) = xy³ ? e????, fx c) f(t, u) = ln(t² - tu), f_t d) f(x,z) = (3t² + 4z) / z², fz
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- To find \( f_y \), use the chain rule: \( f_y = \frac{1}{2}(5x^2 + x^2y - 3y^2)^{-1/2} \cdot \frac{\partial}{\partial y}(5x^2 + x^2y - 3y^2) \). - Calculate the partial derivative inside the chain rule: \( \frac{\partial}{\partial y}(5x^2 + x^2y - 3y^2) = x^2 - Show more…
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