What is (\partial)/(\partial x)(x^8+5xy^9) ?

The answer to (\partial)/(\partial x)(x^8+5xy^9) is 8x^7+5y^9

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(\partial)/(\partial x)(x^8+5xy^9)

\frac{\partial}{\partial x} (x^{8} + 5 x y^{9})

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

Solution steps

\frac{\partial}{\partial x} (x^{8} + 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^{8}) + \frac{\partial}{\partial x} (5 x y^{9})

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

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

= 8 x^{7} + 5 y^{9}

\frac{\partial}{\partial y} (x e^{x^{2} + y^{2}})

\frac{d y}{d x} + x^{2} y = 1

x \to 0 lim (8^{- x})

3 ln (x) - \frac{x ^{2}}{24}

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{x} + e^{2 x} + e^{- x}

What is (\partial)/(\partial x)(x^8+5xy^9) ?
The answer to (\partial)/(\partial x)(x^8+5xy^9) is 8x^7+5y^9