Solve sqrt{48}xsqrt{12}

$$\sqrt { 48 } x \sqrt { 12 }$$

Evaluate

$$24x$$

Solution Steps

Factor 48=12\times 4. Rewrite the square root of the product \sqrt{12\times 4} as the product of square roots \sqrt{12}\sqrt{4}.

$$\sqrt{12}\sqrt{4}x\sqrt{12}$$

Multiply \sqrt{12} and \sqrt{12} to get 12.

$$12x\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$12x\times 2$$

Multiply 12 and 2 to get 24.

$$24x$$

Differentiate w.r.t. x

$$24$$

Steps Using Definition of a Derivative

Factor 48=12\times 4. Rewrite the square root of the product \sqrt{12\times 4} as the product of square roots \sqrt{12}\sqrt{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\sqrt{12}\sqrt{4}x\sqrt{12})$$

Multiply \sqrt{12} and \sqrt{12} to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x\sqrt{4})$$

Calculate the square root of 4 and get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x\times 2)$$

Multiply 12 and 2 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(24x)$$

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

$$24x^{1-1}$$

Subtract 1 from 1.

$$24x^{0}$$

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

$$24\times 1$$

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

$$24$$