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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

y = x^{2} + 3 x + 1, y = - x + 1

\frac{d y}{d x} = \frac{x}{( 1 + 2 y )}

y = \frac{sin ( x ) + cos ( x )}{e ^{x}}

\frac{d}{d x} (- \frac{6 e ^{\frac{6}{x}}}{x ^{2}})

x \cdot cos (x)

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