What is (\partial)/(\partial x)(x^8y^9-x^7y^8) ?

The answer to (\partial)/(\partial x)(x^8y^9-x^7y^8) is 8y^9x^7-7y^8x^6

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(\partial)/(\partial x)(x^8y^9-x^7y^8)

\frac{\partial}{\partial x} (x^{8} y^{9} - x^{7} y^{8})

8 y^{9} x^{7} - 7 y^{8} x^{6}

Solution steps

\frac{\partial}{\partial x} (x^{8} y^{9} - x^{7} y^{8})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{8} y^{9}) - \frac{\partial}{\partial x} (x^{7} y^{8})

\frac{\partial}{\partial x} (x^{8} y^{9}) = 8 y^{9} x^{7}

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

= 8 y^{9} x^{7} - 7 y^{8} x^{6}

\frac{d}{d x} (2 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x))

f (x) = sec (x)

y (θ) = \frac{π}{7} sin (θ)

x \to - 9 - lim (\frac{- 2 x}{x + 9})

\int 2 x^{3} + 5 x^{2} - 2 x + 1 d x

What is (\partial)/(\partial x)(x^8y^9-x^7y^8) ?
The answer to (\partial)/(\partial x)(x^8y^9-x^7y^8) is 8y^9x^7-7y^8x^6