What is (\partial)/(\partial x)(x^8y^6+3x^7y) ?

The answer to (\partial)/(\partial x)(x^8y^6+3x^7y) is 8y^6x^7+21yx^6

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(\partial)/(\partial x)(x^8y^6+3x^7y)

\frac{\partial}{\partial x} (x^{8} y^{6} + 3 x^{7} y)

8 y^{6} x^{7} + 21 y x^{6}

Solution steps

\frac{\partial}{\partial x} (x^{8} y^{6} + 3 x^{7} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{8} y^{6}) + \frac{\partial}{\partial x} (3 x^{7} y)

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

\frac{\partial}{\partial x} (3 x^{7} y) = 21 y x^{6}

= 8 y^{6} x^{7} + 21 y x^{6}

\int (x^{2} x - 5) d x

x \to 0 + lim (\frac{7 x}{sin ( x )})

f (x) = (x^{4} - 2 x + 8)^{6}, at x = 1

\int e^{x^{2}} 2 x^{3} d x

x \to \infty lim (- 5)

What is (\partial)/(\partial x)(x^8y^6+3x^7y) ?
The answer to (\partial)/(\partial x)(x^8y^6+3x^7y) is 8y^6x^7+21yx^6