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

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

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(\partial)/(\partial x)(4x^3+4xy^2)

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

12 x^{2} + 4 y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 12 x^{2} + 4 y^{2}

e^{- 3 t}

(t^{2} + 16) (\frac{d x}{d t}) = (x^{2} + 25), x (0) = 5

x \to 0 lim ((1 - 5 x)^{\frac{1}{x}})

\int tan (x) (sec (x))^{4} d x

\frac{d}{d x} (\frac{x ^{2}}{( x - 1 ) ^{2}})

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