What is (\partial)/(\partial y)(xsqrt(1+y^5)) ?

The answer to (\partial)/(\partial y)(xsqrt(1+y^5)) is (5xy^4)/(2sqrt(1+y^5))

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(\partial)/(\partial y)(xsqrt(1+y^5))

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (1 + y^{5}) = 5 y^{4}

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

Simplify

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

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

What is (\partial)/(\partial y)(xsqrt(1+y^5)) ?
The answer to (\partial)/(\partial y)(xsqrt(1+y^5)) is (5xy^4)/(2sqrt(1+y^5))