What is (\partial)/(\partial x)(2x^4y+sin(x^3)) ?

The answer to (\partial)/(\partial x)(2x^4y+sin(x^3)) is 8yx^3+cos(x^3)*3x^2

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(\partial)/(\partial x)(2x^4y+sin(x^3))

\frac{\partial}{\partial x} (2 x^{4} y + sin (x^{3}))

8 y x^{3} + cos (x^{3}) \cdot 3 x^{2}

Solution steps

\frac{\partial}{\partial x} (2 x^{4} y + sin (x^{3}))

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x^{4} y) + \frac{\partial}{\partial x} (sin (x^{3}))

\frac{\partial}{\partial x} (2 x^{4} y) = 8 y x^{3}

\frac{\partial}{\partial x} (sin (x^{3})) = cos (x^{3}) \cdot 3 x^{2}

= 8 y x^{3} + cos (x^{3}) \cdot 3 x^{2}

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What is (\partial)/(\partial x)(2x^4y+sin(x^3)) ?
The answer to (\partial)/(\partial x)(2x^4y+sin(x^3)) is 8yx^3+cos(x^3)*3x^2