What is (\partial)/(\partial x)(x^9y^4-x^8y^3) ?

The answer to (\partial)/(\partial x)(x^9y^4-x^8y^3) is 9y^4x^8-8y^3x^7

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(\partial)/(\partial x)(x^9y^4-x^8y^3)

\frac{\partial}{\partial x} (x^{9} y^{4} - x^{8} y^{3})

9 y^{4} x^{8} - 8 y^{3} x^{7}

Solution steps

\frac{\partial}{\partial x} (x^{9} y^{4} - x^{8} y^{3})

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^{8} y^{3})

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

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

= 9 y^{4} x^{8} - 8 y^{3} x^{7}

x y^{^{'}} = y + x sin (x)

y^{^{''}} + 2 y^{^{'}} + 5 y = 0

\int \frac{1}{( x + 4 ) ^{3}} d x

y^{^{''}} - 6 y^{^{'}} + 7 y = 0, y (0) = 0, y^{^{'}} (0) = 1

\int \frac{1}{x ( 3 x + 1 )} d x

What is (\partial)/(\partial x)(x^9y^4-x^8y^3) ?
The answer to (\partial)/(\partial x)(x^9y^4-x^8y^3) is 9y^4x^8-8y^3x^7