Solve sqrt{12x^5}*sqrt{12x^5}

$$\sqrt { 12 x ^ { 5 } } \cdot \sqrt { 12 x ^ { 5 } }$$

Evaluate

$$12x^{5}$$

Solution Steps

Multiply \sqrt{12x^{5}} and \sqrt{12x^{5}} to get \left(\sqrt{12x^{5}}\right)^{2}.

$$\left(\sqrt{12x^{5}}\right)^{2}$$

Calculate \sqrt{12x^{5}} to the power of 2 and get 12x^{5}.

$$12x^{5}$$

Differentiate w.r.t. x

$$60x^{4}$$

Steps Using Definition of a Derivative

Multiply \sqrt{12x^{5}} and \sqrt{12x^{5}} to get \left(\sqrt{12x^{5}}\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(\sqrt{12x^{5}}\right)^{2})$$

Calculate \sqrt{12x^{5}} to the power of 2 and get 12x^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{5})$$

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

$$5\times 12x^{5-1}$$

Multiply 5 times 12.

$$60x^{5-1}$$

Subtract 1 from 5.

$$60x^{4}$$