What is (\partial)/(\partial x)(x^4y^9+6x^7y) ?

The answer to (\partial)/(\partial x)(x^4y^9+6x^7y) is 4y^9x^3+42yx^6

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(\partial)/(\partial x)(x^4y^9+6x^7y)

\frac{\partial}{\partial x} (x^{4} y^{9} + 6 x^{7} y)

4 y^{9} x^{3} + 42 y x^{6}

Solution steps

\frac{\partial}{\partial x} (x^{4} y^{9} + 6 x^{7} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{4} y^{9}) + \frac{\partial}{\partial x} (6 x^{7} y)

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

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

= 4 y^{9} x^{3} + 42 y x^{6}

y^{^{'}} - \frac{7}{x} \cdot y = 0

\int \frac{1}{1 - cos ( x ) + sin ( x )} d x

\frac{d}{d x} (\frac{5 x ^{4} + 7 x ^{2} - 3}{2 x ^{2}})

\int 4 x e^{x^{2}} d x

\int 3 y e^{3 z} d z

What is (\partial)/(\partial x)(x^4y^9+6x^7y) ?
The answer to (\partial)/(\partial x)(x^4y^9+6x^7y) is 4y^9x^3+42yx^6