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Differentiate w.r.t. x
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-4\left(-\left(\sqrt{\frac{x}{2}-\frac{3\times 2}{2}}\right)^{2}-3\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.
-4\left(-\left(\sqrt{\frac{x-3\times 2}{2}}\right)^{2}-3\right)
Since \frac{x}{2} and \frac{3\times 2}{2} have the same denominator, subtract them by subtracting their numerators.
-4\left(-\left(\sqrt{\frac{x-6}{2}}\right)^{2}-3\right)
Do the multiplications in x-3\times 2.
-4\left(-\frac{x-6}{2}-3\right)
Calculate \sqrt{\frac{x-6}{2}} to the power of 2 and get \frac{x-6}{2}.
-4\left(-\frac{x-6}{2}-\frac{3\times 2}{2}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.
-4\times \left(\frac{-\left(x-6\right)-3\times 2}{2}\right)
Since -\frac{x-6}{2} and \frac{3\times 2}{2} have the same denominator, subtract them by subtracting their numerators.
-4\times \left(\frac{-x+6-6}{2}\right)
Do the multiplications in -\left(x-6\right)-3\times 2.
-4\times \left(\frac{-x}{2}\right)
Combine like terms in -x+6-6.
-2\left(-1\right)x
Cancel out 2, the greatest common factor in 4 and 2.
2x
Multiply -2 and -1 to get 2.
\frac{\mathrm{d}}{\mathrm{d}x}(-4\left(-\left(\sqrt{\frac{x}{2}-\frac{3\times 2}{2}}\right)^{2}-3\right))
To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.
\frac{\mathrm{d}}{\mathrm{d}x}(-4\left(-\left(\sqrt{\frac{x-3\times 2}{2}}\right)^{2}-3\right))
Since \frac{x}{2} and \frac{3\times 2}{2} have the same denominator, subtract them by subtracting their numerators.
\frac{\mathrm{d}}{\mathrm{d}x}(-4\left(-\left(\sqrt{\frac{x-6}{2}}\right)^{2}-3\right))
Do the multiplications in x-3\times 2.
\frac{\mathrm{d}}{\mathrm{d}x}(-4\left(-\frac{x-6}{2}-3\right))
Calculate \sqrt{\frac{x-6}{2}} to the power of 2 and get \frac{x-6}{2}.
\frac{\mathrm{d}}{\mathrm{d}x}(-4\left(-\frac{x-6}{2}-\frac{3\times 2}{2}\right))
To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.
\frac{\mathrm{d}}{\mathrm{d}x}(-4\times \left(\frac{-\left(x-6\right)-3\times 2}{2}\right))
Since -\frac{x-6}{2} and \frac{3\times 2}{2} have the same denominator, subtract them by subtracting their numerators.
\frac{\mathrm{d}}{\mathrm{d}x}(-4\times \left(\frac{-x+6-6}{2}\right))
Do the multiplications in -\left(x-6\right)-3\times 2.
\frac{\mathrm{d}}{\mathrm{d}x}(-4\times \left(\frac{-x}{2}\right))
Combine like terms in -x+6-6.
\frac{\mathrm{d}}{\mathrm{d}x}(-2\left(-1\right)x)
Cancel out 2, the greatest common factor in 4 and 2.
\frac{\mathrm{d}}{\mathrm{d}x}(2x)
Multiply -2 and -1 to get 2.
2x^{1-1}
The derivative of ax^{n} is nax^{n-1}.
2x^{0}
Subtract 1 from 1.
2\times 1
For any term t except 0, t^{0}=1.
2
For any term t, t\times 1=t and 1t=t.