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

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

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(\partial)/(\partial x)(sqrt(x^5+y^7))

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

\frac{5 x ^{4}}{2 x ^{5} + y ^{7}}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{2 x ^{5} + y ^{7}} \cdot 5 x^{4}

Simplify

\frac{1}{2 x ^{5} + y ^{7}} \cdot 5 x^{4} : \frac{5 x ^{4}}{2 x ^{5} + y ^{7}}

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

\int 1 + (\frac{1}{2 x} - \frac{x}{2})^{2} d x

y^{^{''}} + 9 y = 6 sin (3 t)

2 sec (x)

\frac{d}{d x} (4^{2 - 2 x})

\int_{0}^{1} 2 x (4 - x^{2}) d x

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