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

The answer to (\partial)/(\partial w)((y-w(x+x^2))^2) is 2(y-w(x+x^2))(-x^2-x)

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(\partial)/(\partial w)((y-w(x+x^2))^2)

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

2 (y - w (x + x^{2})) (- x^{2} - x)

Solution steps

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

Treat

y, x

as constants

Apply the chain rule:

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

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

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

= 2 (y - w (x + x^{2})) (- x^{2} - x)

x \to \frac{1}{2} lim (\frac{1}{2 x - 1})

\int \frac{( x ^{3} )}{x ^{2} + 36} d x

x^{2} \frac{d y}{d x} = \frac{1}{4} x^{2} + y^{2}

t \to 0 lim (e^{- 7 t} i + \frac{t ^{2}}{sin ^{2} ( t )} j + tan (3 t k))

f (x) = sin (x^{2} + 1)

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