What is (\partial)/(\partial x)(5x^3+4xy^3) ?

The answer to (\partial)/(\partial x)(5x^3+4xy^3) is 15x^2+4y^3

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(\partial)/(\partial x)(5x^3+4xy^3)

\frac{\partial}{\partial x} (5 x^{3} + 4 x y^{3})

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

Solution steps

\frac{\partial}{\partial x} (5 x^{3} + 4 x y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (5 x^{3}) + \frac{\partial}{\partial x} (4 x y^{3})

\frac{\partial}{\partial x} (5 x^{3}) = 15 x^{2}

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

= 15 x^{2} + 4 y^{3}

\int \frac{x ^{2} + 1}{x} d x

n = 1 \sum \infty \frac{x ^{n - 1}}{x}

x \to 1 lim (- 1 x^{- 1 - 1} sin (\frac{1}{x}) - x^{- 1 - 2} cos (\frac{1}{x}))

l a pl a ce t r an s f or m 2 t + 3

a re a y = x, y = x^{2}

What is (\partial)/(\partial x)(5x^3+4xy^3) ?
The answer to (\partial)/(\partial x)(5x^3+4xy^3) is 15x^2+4y^3