What is (\partial)/(\partial x)(7xy^9+x^5y^7) ?

The answer to (\partial)/(\partial x)(7xy^9+x^5y^7) is 7y^9+5y^7x^4

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(\partial)/(\partial x)(7xy^9+x^5y^7)

\frac{\partial}{\partial x} (7 x y^{9} + x^{5} y^{7})

7 y^{9} + 5 y^{7} x^{4}

Solution steps

\frac{\partial}{\partial x} (7 x y^{9} + 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 y^{9}) + \frac{\partial}{\partial x} (x^{5} y^{7})

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

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

= 7 y^{9} + 5 y^{7} x^{4}

\frac{d}{d x} (2 x + \frac{4}{x})

\int \frac{18}{1 - cos ( 2 x )} d x

\int \frac{5 x ^{4}}{( 10 + x ^{5} ) ^{4}} d x

\int \frac{sin ( x )}{sec ( x )} d x

\int_{0}^{2} \frac{1}{( x - 2 ) ^{2}} d x

What is (\partial)/(\partial x)(7xy^9+x^5y^7) ?
The answer to (\partial)/(\partial x)(7xy^9+x^5y^7) is 7y^9+5y^7x^4