What is (\partial)/(\partial x)(4xy^8+x^3y^2) ?

The answer to (\partial)/(\partial x)(4xy^8+x^3y^2) is 4y^8+3y^2x^2

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(\partial)/(\partial x)(4xy^8+x^3y^2)

\frac{\partial}{\partial x} (4 x y^{8} + x^{3} y^{2})

4 y^{8} + 3 y^{2} x^{2}

Solution steps

\frac{\partial}{\partial x} (4 x y^{8} + x^{3} y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 x y^{8}) + \frac{\partial}{\partial x} (x^{3} y^{2})

\frac{\partial}{\partial x} (4 x y^{8}) = 4 y^{8}

\frac{\partial}{\partial x} (x^{3} y^{2}) = 3 y^{2} x^{2}

= 4 y^{8} + 3 y^{2} x^{2}

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

\int \frac{1}{4 + x ^{2}} d x

f (x) = 2 x ln (3 x) - 2 x

\int (x - 1)^{2} x^{3} (2 - x) d x

x \to - \infty lim (\frac{4}{x} - 12)

What is (\partial)/(\partial x)(4xy^8+x^3y^2) ?
The answer to (\partial)/(\partial x)(4xy^8+x^3y^2) is 4y^8+3y^2x^2