What is the derivative of (x-ap-p^2) ?

The derivative of (x-ap-p^2) is p+(dp)/(dx)(x-a)-2p(dp)/(dx)

What is the first derivative of (x-ap-p^2) ?

The first derivative of (x-ap-p^2) is p+(dp)/(dx)(x-a)-2p(dp)/(dx)

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\frac{d}{d x} ((x - a) p (x) - p (x)^{2})

p + \frac{d p}{d x} (x - a) - 2 p \frac{d p}{d x}

Solution steps

\frac{d}{d x} ((x - a) p - p^{2})

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} ((x - a) p) = p + \frac{d p}{d x} (x - a)

\frac{d}{d x} (p^{2}) = 2 p \frac{d p}{d x}

= p + \frac{d p}{d x} (x - a) - 2 p \frac{d p}{d x}

What is the derivative of (x-ap-p^2) ?
The derivative of (x-ap-p^2) is p+(dp)/(dx)(x-a)-2p(dp)/(dx)
What is the first derivative of (x-ap-p^2) ?
The first derivative of (x-ap-p^2) is p+(dp)/(dx)(x-a)-2p(dp)/(dx)