Solve -4(-{left(sqrt{(xdiv2)-3}right)}^2-3

$$-4(- { \left( \sqrt{ (x \div 2)-3 } \right) }^{ 2 } -3$$

Evaluate

$$2x$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

$$-4\left(-\left(\sqrt{\frac{x}{2}-\frac{3\times 2}{2}}\right)^{2}-3\right)$$

Since \frac{x}{2} and \frac{3\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$-4\left(-\left(\sqrt{\frac{x-3\times 2}{2}}\right)^{2}-3\right)$$

Do the multiplications in x-3\times 2.

$$-4\left(-\left(\sqrt{\frac{x-6}{2}}\right)^{2}-3\right)$$

Calculate \sqrt{\frac{x-6}{2}} to the power of 2 and get \frac{x-6}{2}.

$$-4\left(-\frac{x-6}{2}-3\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

$$-4\left(-\frac{x-6}{2}-\frac{3\times 2}{2}\right)$$

Since -\frac{x-6}{2} and \frac{3\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$-4\times \frac{-\left(x-6\right)-3\times 2}{2}$$

Do the multiplications in -\left(x-6\right)-3\times 2.

$$-4\times \frac{-x+6-6}{2}$$

Combine like terms in -x+6-6.

$$-4\times \frac{-x}{2}$$

Cancel out 2, the greatest common factor in 4 and 2.

$$-2\left(-1\right)x$$

Multiply -2 and -1 to get 2.

$$2x$$

Differentiate w.r.t. x

$$2$$

Steps Using Definition of a Derivative

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4\left(-\left(\sqrt{\frac{x}{2}-\frac{3\times 2}{2}}\right)^{2}-3\right))$$

Since \frac{x}{2} and \frac{3\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4\left(-\left(\sqrt{\frac{x-3\times 2}{2}}\right)^{2}-3\right))$$

Do the multiplications in x-3\times 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4\left(-\left(\sqrt{\frac{x-6}{2}}\right)^{2}-3\right))$$

Calculate \sqrt{\frac{x-6}{2}} to the power of 2 and get \frac{x-6}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4\left(-\frac{x-6}{2}-3\right))$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4\left(-\frac{x-6}{2}-\frac{3\times 2}{2}\right))$$

Since -\frac{x-6}{2} and \frac{3\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4\times \frac{-\left(x-6\right)-3\times 2}{2})$$

Do the multiplications in -\left(x-6\right)-3\times 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4\times \frac{-x+6-6}{2})$$

Combine like terms in -x+6-6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4\times \frac{-x}{2})$$

Cancel out 2, the greatest common factor in 4 and 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2\left(-1\right)x)$$

Multiply -2 and -1 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x)$$

The derivative of ax^{n} is nax^{n-1}.

$$2x^{1-1}$$

Subtract 1 from 1.

$$2x^{0}$$

For any term t except 0, t^{0}=1.

$$2\times 1$$

For any term t, t\times 1=t and 1t=t.

$$2$$