What is (\partial)/(\partial x)(x^4y^6+4x^7y) ?

The answer to (\partial)/(\partial x)(x^4y^6+4x^7y) is 4y^6x^3+28yx^6

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(\partial)/(\partial x)(x^4y^6+4x^7y)

\frac{\partial}{\partial x} (x^{4} y^{6} + 4 x^{7} y)

4 y^{6} x^{3} + 28 y x^{6}

Solution steps

\frac{\partial}{\partial x} (x^{4} y^{6} + 4 x^{7} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{4} y^{6}) + \frac{\partial}{\partial x} (4 x^{7} y)

\frac{\partial}{\partial x} (x^{4} y^{6}) = 4 y^{6} x^{3}

\frac{\partial}{\partial x} (4 x^{7} y) = 28 y x^{6}

= 4 y^{6} x^{3} + 28 y x^{6}

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = x - 3 e^{x}

t^{2} e^{2 t}

\int_{- 7}^{7} x 49 - x^{2} d x

d y - d x + y = e^{4 x}

\int_{- 2}^{3} \frac{49}{x ^{4}} d x

What is (\partial)/(\partial x)(x^4y^6+4x^7y) ?
The answer to (\partial)/(\partial x)(x^4y^6+4x^7y) is 4y^6x^3+28yx^6