What is (\partial)/(\partial x)(x^4y^8+4x^5y) ?

The answer to (\partial)/(\partial x)(x^4y^8+4x^5y) is 4y^8x^3+20yx^4

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(\partial)/(\partial x)(x^4y^8+4x^5y)

\frac{\partial}{\partial x} (x^{4} y^{8} + 4 x^{5} y)

4 y^{8} x^{3} + 20 y x^{4}

Solution steps

\frac{\partial}{\partial x} (x^{4} y^{8} + 4 x^{5} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{4} y^{8}) + \frac{\partial}{\partial x} (4 x^{5} y)

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

\frac{\partial}{\partial x} (4 x^{5} y) = 20 y x^{4}

= 4 y^{8} x^{3} + 20 y x^{4}

ln (\frac{x}{x ^{2} + 2})

\frac{d}{d x} (5 lo g_{2} (x))

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 0, y (\frac{π}{2}) = 1

\frac{8}{( s - 1 ) ^{3}}

y^{^{'}} = \frac{1}{1 + x}

What is (\partial)/(\partial x)(x^4y^8+4x^5y) ?
The answer to (\partial)/(\partial x)(x^4y^8+4x^5y) is 4y^8x^3+20yx^4