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

The answer to (\partial)/(\partial x)(4x-3x^4y^2) is 4-12y^2x^3

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(\partial)/(\partial x)(4x-3x^4y^2)

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

4 - 12 y^{2} x^{3}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (3 x^{4} y^{2}) = 12 y^{2} x^{3}

= 4 - 12 y^{2} x^{3}

\int \frac{t ^{5}}{t ^{2} + 2} d t

\int \frac{1}{y ^{\frac{3}{2}}} d y

e^{1 - x^{2}}

\frac{\partial}{\partial z} (y \cdot arctan (\frac{x}{z}))

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

What is (\partial)/(\partial x)(4x-3x^4y^2) ?
The answer to (\partial)/(\partial x)(4x-3x^4y^2) is 4-12y^2x^3