What is (\partial)/(\partial x)(7x^6y^4+8x^5y^7) ?

The answer to (\partial)/(\partial x)(7x^6y^4+8x^5y^7) is 42y^4x^5+40y^7x^4

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(\partial)/(\partial x)(7x^6y^4+8x^5y^7)

\frac{\partial}{\partial x} (7 x^{6} y^{4} + 8 x^{5} y^{7})

42 y^{4} x^{5} + 40 y^{7} x^{4}

Solution steps

\frac{\partial}{\partial x} (7 x^{6} y^{4} + 8 x^{5} y^{7})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (7 x^{6} y^{4}) + \frac{\partial}{\partial x} (8 x^{5} y^{7})

\frac{\partial}{\partial x} (7 x^{6} y^{4}) = 42 y^{4} x^{5}

\frac{\partial}{\partial x} (8 x^{5} y^{7}) = 40 y^{7} x^{4}

= 42 y^{4} x^{5} + 40 y^{7} x^{4}

\int \frac{( 2 x ^{2} - x + 4 )}{x ^{3} + 4 x} d x

x \to 2 lim (\frac{x ^{3} + x ^{2} - 8 x - 12}{x ^{4} + 4 x ^{3} + 5 x ^{2} + 4 x + 4})

\frac{\partial}{\partial x} (z^{3} - x y + yz + y^{3} - 2)

\frac{4}{[ s ( s ^{2} + 4 ) ]}

y^{^{'}} = \frac{( t ^{4} + y ^{4} )}{t y ^{3}}

What is (\partial)/(\partial x)(7x^6y^4+8x^5y^7) ?
The answer to (\partial)/(\partial x)(7x^6y^4+8x^5y^7) is 42y^4x^5+40y^7x^4