What is the derivative of 100(y-x^2^2+(1-x)^2) ?

The derivative of 100(y-x^2^2+(1-x)^2) is 200(y-x^2)((dy)/(dx)-2x)-2(1-x)

What is the first derivative of 100(y-x^2^2+(1-x)^2) ?

The first derivative of 100(y-x^2^2+(1-x)^2) is 200(y-x^2)((dy)/(dx)-2x)-2(1-x)

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\frac{d}{d x} (100 (y - x^{2})^{2} + (1 - x)^{2})

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

Solution steps

\frac{d}{d x} (100 (y - x^{2})^{2} + (1 - x)^{2})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (100 (y - x^{2})^{2}) + \frac{d}{d x} ((1 - x)^{2})

\frac{d}{d x} (100 (y - x^{2})^{2}) = 200 (y - x^{2}) (\frac{d y}{d x} - 2 x)

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

= 200 (y - x^{2}) (\frac{d y}{d x} - 2 x) - 2 (1 - x)

What is the derivative of 100(y-x^2^2+(1-x)^2) ?
The derivative of 100(y-x^2^2+(1-x)^2) is 200(y-x^2)((dy)/(dx)-2x)-2(1-x)
What is the first derivative of 100(y-x^2^2+(1-x)^2) ?
The first derivative of 100(y-x^2^2+(1-x)^2) is 200(y-x^2)((dy)/(dx)-2x)-2(1-x)