What is (\partial)/(\partial x)(sqrt(6-x^7-y^5)) ?

The answer to (\partial)/(\partial x)(sqrt(6-x^7-y^5)) is -(7x^6)/(2sqrt(6-x^7-y^5))

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(\partial)/(\partial x)(sqrt(6-x^7-y^5))

\frac{\partial}{\partial x} (6 - x^{7} - y^{5})

- \frac{7 x ^{6}}{2 6 - x ^{7} - y ^{5}}

Solution steps

\frac{\partial}{\partial x} (6 - x^{7} - y^{5})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 6 - x ^{7} - y ^{5}} \frac{\partial}{\partial x} (6 - x^{7} - y^{5})

= \frac{1}{2 6 - x ^{7} - y ^{5}} \frac{\partial}{\partial x} (6 - x^{7} - y^{5})

\frac{\partial}{\partial x} (6 - x^{7} - y^{5}) = - 7 x^{6}

= \frac{1}{2 6 - x ^{7} - y ^{5}} (- 7 x^{6})

Simplify

\frac{1}{2 6 - x ^{7} - y ^{5}} (- 7 x^{6}) : - \frac{7 x ^{6}}{2 6 - x ^{7} - y ^{5}}

= - \frac{7 x ^{6}}{2 6 - x ^{7} - y ^{5}}

\frac{d}{d x} (arctan (x + 2))

\frac{d}{d x} (sin (x - y))

\int \frac{20 x ^{3}}{3 + 5 x ^{4}} d x

\frac{\partial}{\partial x} (x^{2} - y^{2} + 2 x y)

(7 x^{3} + x^{2})^{\frac{2}{3}}

What is (\partial)/(\partial x)(sqrt(6-x^7-y^5)) ?
The answer to (\partial)/(\partial x)(sqrt(6-x^7-y^5)) is -(7x^6)/(2sqrt(6-x^7-y^5))