What is (\partial)/(\partial x)(x^4+2xy^9) ?

The answer to (\partial)/(\partial x)(x^4+2xy^9) is 4x^3+2y^9

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(\partial)/(\partial x)(x^4+2xy^9)

\frac{\partial}{\partial x} (x^{4} + 2 x y^{9})

4 x^{3} + 2 y^{9}

Solution steps

\frac{\partial}{\partial x} (x^{4} + 2 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} (2 x y^{9})

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

\frac{\partial}{\partial x} (2 x y^{9}) = 2 y^{9}

= 4 x^{3} + 2 y^{9}

\frac{d}{d x} ((x y)^{2})

\frac{- x sin ( x ) - cos ( x )}{4 x ^{2}}

\int x^{2} - 6 x + 5 d x

\frac{\partial}{\partial x} (2 x^{2} + 5 y^{2})

y = 2 x^{3} - 2 x (- 1)

What is (\partial)/(\partial x)(x^4+2xy^9) ?
The answer to (\partial)/(\partial x)(x^4+2xy^9) is 4x^3+2y^9