Get the answer to "Find the first partial derivatives. g(x,y)=ln⁡(x6+y6) gx(x,y)= gy(x,y)=" - Plainmath

Nannie Mack

Answered question

2021-11-10

Find the first partial derivatives.

g (x, y) = \ln (x^{6} + y^{6})

g_{x} (x, y) =

g_{y} (x, y) =

Answer & Explanation

SkladanH

Skilled2021-11-11Added 80 answers

Step 1

g (x, y) = \ln (x^{6} + y^{6})

Step 2

g_{x} (x, y) = \frac{d}{d x} (\ln (x^{6} + y^{6}))

g_{x} (x, y) = \frac{1}{x^{6} + y^{6}} \cdot 6 x^{5}

g_{x} (x, y) = \frac{6 x^{5}}{x^{6} + y^{6}}

g_{y} (x, y) = \frac{d}{d x} (\ln (x^{6} + y^{6}))

= \frac{1}{x^{6} + y^{6}} \cdot 6 y^{5}

g_{y} (x, y) = \frac{6 y^{5}}{x^{6} + y^{6}}

g_{x} (x, y) = \frac{6 x^{5}}{x^{6} + y^{6}}

g_{y} (x, y) = \frac{6 y^{5}}{x^{6} + y^{6}}

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