What is (\partial)/(\partial x)(x^4+5xy^9) ?

The answer to (\partial)/(\partial x)(x^4+5xy^9) is 4x^3+5y^9

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(\partial)/(\partial x)(x^4+5xy^9)

\frac{\partial}{\partial x} (x^{4} + 5 x y^{9})

4 x^{3} + 5 y^{9}

Solution steps

\frac{\partial}{\partial x} (x^{4} + 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^{4}) + \frac{\partial}{\partial x} (5 x y^{9})

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

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

= 4 x^{3} + 5 y^{9}

t \to 0 lim (t^{2})

\frac{\partial}{\partial y} (x ln (x + 2 y))

\frac{d}{d t} ((t + sin (t - 1))^{3} (t^{2} - 2)^{5})

\int x \cdot ln (x^{2} + 1) d x

\int_{0}^{1} ln (2 x + 1) d x

What is (\partial)/(\partial x)(x^4+5xy^9) ?
The answer to (\partial)/(\partial x)(x^4+5xy^9) is 4x^3+5y^9