Solve ((x^2)^3)^2

$$( ( x ^ { 2 } ) ^ { 3 } ) ^ { 2 }$$

Evaluate

$$x^{12}$$

Steps for Raising Power to Another Power

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(x^{6}\right)^{2}$$

To raise a power to another power, multiply the exponents.

$$x^{6\times 2}$$

Multiply 6 times 2.

$$x^{12}$$

Differentiate w.r.t. x

$$12x^{11}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x^{6}\right)^{2})$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

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

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

$$12x^{12-1}$$

Subtract 1 from 12.

$$12x^{11}$$