What is (\partial)/(\partial x)(sqrt(1-x^7-y^7)) ?

The answer to (\partial)/(\partial x)(sqrt(1-x^7-y^7)) is -(7x^6)/(2sqrt(1-x^7-y^7))

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(\partial)/(\partial x)(sqrt(1-x^7-y^7))

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

- \frac{7 x ^{6}}{2 1 - x ^{7} - y ^{7}}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

θ \to 0 lim (sin (θ) ln (θ))

f (x) = \frac{x ^{2} - 1}{x}

\frac{d}{d x} (1 5^{x})

\int x cos (2 π) x^{2} d x

x \to - 6 lim (x)

What is (\partial)/(\partial x)(sqrt(1-x^7-y^7)) ?
The answer to (\partial)/(\partial x)(sqrt(1-x^7-y^7)) is -(7x^6)/(2sqrt(1-x^7-y^7))