What is (\partial)/(\partial x)(sqrt(7-x^5-y^3)) ?

The answer to (\partial)/(\partial x)(sqrt(7-x^5-y^3)) is -(5x^4)/(2sqrt(7-x^5-y^3))

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(\partial)/(\partial x)(sqrt(7-x^5-y^3))

\frac{\partial}{\partial x} (7 - x^{5} - y^{3})

- \frac{5 x ^{4}}{2 7 - x ^{5} - y ^{3}}

Solution steps

\frac{\partial}{\partial x} (7 - x^{5} - y^{3})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 7 - x ^{5} - y ^{3}} \frac{\partial}{\partial x} (7 - x^{5} - y^{3})

= \frac{1}{2 7 - x ^{5} - y ^{3}} \frac{\partial}{\partial x} (7 - x^{5} - y^{3})

\frac{\partial}{\partial x} (7 - x^{5} - y^{3}) = - 5 x^{4}

= \frac{1}{2 7 - x ^{5} - y ^{3}} (- 5 x^{4})

Simplify

\frac{1}{2 7 - x ^{5} - y ^{3}} (- 5 x^{4}) : - \frac{5 x ^{4}}{2 7 - x ^{5} - y ^{3}}

= - \frac{5 x ^{4}}{2 7 - x ^{5} - y ^{3}}

\frac{\partial}{\partial u} (x^{5} v^{2} + 2 y^{3} u - 3)

\frac{\partial}{\partial x} (61 - x^{2} - 3 y^{2})

\int_{2}^{5} x^{2} d x

x \to 0 + lim (7 sin (x) ln (x))

\int sin (11 x) ln (sin (11 x)) d x

What is (\partial)/(\partial x)(sqrt(7-x^5-y^3)) ?
The answer to (\partial)/(\partial x)(sqrt(7-x^5-y^3)) is -(5x^4)/(2sqrt(7-x^5-y^3))