What is (\partial)/(\partial x)(8xy^5+x^8y^2) ?

The answer to (\partial)/(\partial x)(8xy^5+x^8y^2) is 8y^5+8y^2x^7

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(\partial)/(\partial x)(8xy^5+x^8y^2)

\frac{\partial}{\partial x} (8 x y^{5} + x^{8} y^{2})

8 y^{5} + 8 y^{2} x^{7}

Solution steps

\frac{\partial}{\partial x} (8 x y^{5} + x^{8} y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (8 x y^{5}) + \frac{\partial}{\partial x} (x^{8} y^{2})

\frac{\partial}{\partial x} (8 x y^{5}) = 8 y^{5}

\frac{\partial}{\partial x} (x^{8} y^{2}) = 8 y^{2} x^{7}

= 8 y^{5} + 8 y^{2} x^{7}

2 y^{^{'''}} + 3 y^{^{''}} - 8 y^{^{'}} + 3 y = 0

\frac{x ^{2}}{4}

\int_{4}^{6} 2 π (y) (\frac{4}{y}) d y

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

\int \frac{1}{24} x d x

What is (\partial)/(\partial x)(8xy^5+x^8y^2) ?
The answer to (\partial)/(\partial x)(8xy^5+x^8y^2) is 8y^5+8y^2x^7