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

The answer to (\partial)/(\partial x)(x^3*4x+5y) is 16x^3

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(\partial)/(\partial x)(x^3*4x+5y)

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

16 x^{3}

Solution steps

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

Simplify

x^{3} \cdot 4 x + 5 y : 4 x^{4} + 5 y

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (4 x^{4}) = 16 x^{3}

\frac{\partial}{\partial x} (5 y) = 0

= 16 x^{3} + 0

Simplify

= 16 x^{3}

y = x (x - 4)

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What is (\partial)/(\partial x)(x^3*4x+5y) ?
The answer to (\partial)/(\partial x)(x^3*4x+5y) is 16x^3