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

The answer to (\partial)/(\partial x)((y)(3x^2+y^2)^3) is 18yx(3x^2+y^2)^2

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

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

18 y x (3 x^{2} + y^{2})^{2}

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (3 x^{2} + y^{2}) = 6 x

= y \cdot 3 (3 x^{2} + y^{2})^{2} \cdot 6 x

Simplify

= 18 y x (3 x^{2} + y^{2})^{2}

\frac{1 - x + 3}{( x + 2 ) ^{2}}

(t + e^{- 2 t})^{2}

(e - 3 x) d x

(x - 6) (x + 3)^{'}

(8 + k) (x - 0, y - 2)

What is (\partial)/(\partial x)((y)(3x^2+y^2)^3) ?
The answer to (\partial)/(\partial x)((y)(3x^2+y^2)^3) is 18yx(3x^2+y^2)^2