What is (\partial)/(\partial x)(x^6+5xy^9) ?

The answer to (\partial)/(\partial x)(x^6+5xy^9) is 6x^5+5y^9

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(\partial)/(\partial x)(x^6+5xy^9)

\frac{\partial}{\partial x} (x^{6} + 5 x y^{9})

6 x^{5} + 5 y^{9}

Solution steps

\frac{\partial}{\partial x} (x^{6} + 5 x y^{9})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{6}) + \frac{\partial}{\partial x} (5 x y^{9})

\frac{\partial}{\partial x} (x^{6}) = 6 x^{5}

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

= 6 x^{5} + 5 y^{9}

\frac{d}{d x} (\frac{8 x ^{3} - 2 x + 9}{x})

\frac{d}{d x} (\frac{1}{4 x ^{3} + 5 x ^{2} - 7 x + 8})

\int x (x^{2} + 3)^{7} d x

\frac{d}{d x} (x^{2} e n (x))

y = tan (3 x)

What is (\partial)/(\partial x)(x^6+5xy^9) ?
The answer to (\partial)/(\partial x)(x^6+5xy^9) is 6x^5+5y^9