What is (\partial)/(\partial x)(1-(x^2+y^2)^{1/7}) ?

The answer to (\partial)/(\partial x)(1-(x^2+y^2)^{1/7}) is -(2x)/(7(x^2+y^2)^{6/7)}

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(\partial)/(\partial x)(1-(x^2+y^2)^{1/7})

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

- \frac{2 x}{7 ( x ^{2} + y ^{2} ) ^{\frac{6}{7}}}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (1) = 0

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

= 0 - \frac{2 x}{7 ( x ^{2} + y ^{2} ) ^{\frac{6}{7}}}

Simplify

= - \frac{2 x}{7 ( x ^{2} + y ^{2} ) ^{\frac{6}{7}}}

x \to 3 - lim (e^{\frac{7}{( x - 3 )}})

\frac{d}{d x} (\frac{e ^{x^{2}}}{2 x})

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

\frac{d}{d x} (e^{- x^{2} - y^{2}})

\int arccsc (x) d x

What is (\partial)/(\partial x)(1-(x^2+y^2)^{1/7}) ?
The answer to (\partial)/(\partial x)(1-(x^2+y^2)^{1/7}) is -(2x)/(7(x^2+y^2)^{6/7)}