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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} ((x y)^{0.5})

y^{^{'}} + sin (t) y = - sin (t), y (0) = 3

80 t^{2}

f (x) = x^{2} (1 - x)^{2}, at x = 2

x \to 0 lim (\frac{( x - 1 ) ^{2} + 1}{x})

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