"Compute the partial derivatives. z=ln⁡(8x2+5y2) ∂z∂x=ln⁡(16x+5y2) ∂z∂y=" was answered by our community

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ka1leE

Answered question

2021-11-06

Compute the partial derivatives.
$z = \ln (8 x^{2} + 5 y^{2})$
$\frac{\partial z}{\partial x} = \ln (16 x + 5 y^{2})$
$\frac{\partial z}{\partial y} =$

Answer & Explanation

Tuthornt

Skilled2021-11-07Added 107 answers

Step 1

z = \ln (8 x^{2} + 5 y^{2})

\frac{\partial z}{\partial x} = \frac{\partial}{\partial x} \ln (8 x^{2} + 5 y^{2})

= \frac{1}{(8 x^{2} + 5 y^{2})} \cdot (8 \times 2 x + 0)

= \frac{16 x}{(8 x^{2} + 5 y^{2})}

Step 2

z = \ln (8 x^{2} + 5 y^{2})

\frac{\partial z}{\partial y} = \frac{\partial}{\partial y} \ln (8 x^{2} + 5 y^{2})

= \frac{1}{(8 x^{2} + 5 y^{2})} \cdot (0 + 5 \times 2 y)

= \frac{10 y}{(8 x^{2} + 5 y^{2})}

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