Solve 2left(x^2right)^3

$$2 { \left( { x }^{ 2 } \right) }^{ 3 }$$

Differentiate w.r.t. x

$$12x^{5}$$

Steps Using Definition of a Derivative

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

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

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

$$6\times 2x^{6-1}$$

Multiply 6 times 2.

$$12x^{6-1}$$

Subtract 1 from 6.

$$12x^{5}$$

Evaluate

$$2x^{6}$$

Solution Steps

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

$$2x^{6}$$