What is the derivative of (x^2-2(m-n)-2m+2n) ?

The derivative of (x^2-2(m-n)-2m+2n) is 2mx-2nx

What is the first derivative of (x^2-2(m-n)-2m+2n) ?

The first derivative of (x^2-2(m-n)-2m+2n) is 2mx-2nx

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\frac{d}{d x} ((x^{2} - 2) (m - n) - 2 m + 2 n)

2 m x - 2 n x

Solution steps

\frac{d}{d x} ((x^{2} - 2) (m - n) - 2 m + 2 n)

Simplify

(x^{2} - 2) (m - n) - 2 m + 2 n : m x^{2} - n x^{2} - 4 m + 4 n

= \frac{d}{d x} (m x^{2} - n x^{2} - 4 m + 4 n)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (m x^{2}) - \frac{d}{d x} (n x^{2}) - \frac{d}{d x} (4 m) + \frac{d}{d x} (4 n)

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

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

\frac{d}{d x} (4 m) = 0

\frac{d}{d x} (4 n) = 0

= 2 m x - 2 n x - 0 + 0

Simplify

= 2 m x - 2 n x

2^{x} - x^{2}

(x^{2} + 3 x)^{5}

\frac{d}{d x} (\frac{( 4 x - y )}{( 2 x + y )})

sin (x^{\frac{1}{2}})

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

What is the derivative of (x^2-2(m-n)-2m+2n) ?
The derivative of (x^2-2(m-n)-2m+2n) is 2mx-2nx
What is the first derivative of (x^2-2(m-n)-2m+2n) ?
The first derivative of (x^2-2(m-n)-2m+2n) is 2mx-2nx