What is (\partial)/(\partial x)(x^9y^4-x^6+y^8) ?

The answer to (\partial)/(\partial x)(x^9y^4-x^6+y^8) is 9x^8y^4-6x^5

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(\partial)/(\partial x)(x^9y^4-x^6+y^8)

\frac{\partial}{\partial x} (x^{9} y^{4} - x^{6} + y^{8})

9 x^{8} y^{4} - 6 x^{5}

Solution steps

\frac{\partial}{\partial x} (x^{9} y^{4} - x^{6} + y^{8})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{9} y^{4}) - \frac{\partial}{\partial x} (x^{6}) + \frac{\partial}{\partial x} (y^{8})

\frac{\partial}{\partial x} (x^{9} y^{4}) = 9 y^{4} x^{8}

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

\frac{\partial}{\partial x} (y^{8}) = 0

= 9 y^{4} x^{8} - 6 x^{5} + 0

Simplify

= 9 x^{8} y^{4} - 6 x^{5}

(- 5, 1), (- 4, - 7)

\frac{x}{e ^{x}}

n = 0 \sum \infty (- 1)^{n + 1}

- 7

y = t e^{- t}

What is (\partial)/(\partial x)(x^9y^4-x^6+y^8) ?
The answer to (\partial)/(\partial x)(x^9y^4-x^6+y^8) is 9x^8y^4-6x^5