What is (\partial)/(\partial y)(xsqrt(1+y^7)) ?

The answer to (\partial)/(\partial y)(xsqrt(1+y^7)) is (7xy^6)/(2sqrt(1+y^7))

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(\partial)/(\partial y)(xsqrt(1+y^7))

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

x \frac{1}{2 1 + y ^{7}} \cdot 7 y^{6} : \frac{7 x y ^{6}}{2 1 + y ^{7}}

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

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What is (\partial)/(\partial y)(xsqrt(1+y^7)) ?
The answer to (\partial)/(\partial y)(xsqrt(1+y^7)) is (7xy^6)/(2sqrt(1+y^7))