What is (\partial)/(\partial x)(x^6y^8+7x^8y) ?

The answer to (\partial)/(\partial x)(x^6y^8+7x^8y) is 6y^8x^5+56yx^7

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(\partial)/(\partial x)(x^6y^8+7x^8y)

\frac{\partial}{\partial x} (x^{6} y^{8} + 7 x^{8} y)

6 y^{8} x^{5} + 56 y x^{7}

Solution steps

\frac{\partial}{\partial x} (x^{6} y^{8} + 7 x^{8} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{6} y^{8}) + \frac{\partial}{\partial x} (7 x^{8} y)

\frac{\partial}{\partial x} (x^{6} y^{8}) = 6 y^{8} x^{5}

\frac{\partial}{\partial x} (7 x^{8} y) = 56 y x^{7}

= 6 y^{8} x^{5} + 56 y x^{7}

- \frac{y}{x}

(3 x + 6 y) d x + (6 x - 8 y 3) d y = 0

x \to 0 lim (x^{2} cos (\frac{3}{x}))

\int x (3 x^{2} + 5)^{3} d x

\int \frac{5 x + 5}{4 x ^{2} + 17 x + 4} d x

What is (\partial)/(\partial x)(x^6y^8+7x^8y) ?
The answer to (\partial)/(\partial x)(x^6y^8+7x^8y) is 6y^8x^5+56yx^7