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(Solved): a and b please; 1. Find the partial derivatives for the following functions: (a) f(x,y)=(4xy2)3/2 ...

$1. Find the partial derivatives for the following functions: (a) \( f(x, y)=\left(4 x-y^{2}\right)^{3 / 2} \) (b) \( f(x, y)=$

a and b please;

1. Find the partial derivatives for the following functions: (a)

f (x, y) = (4 x - y^{2})^{3/2}

(b)

f (x, y) = \frac{x ^{2} - y ^{2}}{x y}

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(a)
Differentiating partially with respect to x



By using the chain rule :

Take



Using the power rule:


Substitute back

While differentiating partially with respect to x take y as constant

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