Solve d/dxleft(2left(x^2right)^2right)

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

Evaluate

$$8x^{3}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

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

$$4\times 2x^{4-1}$$

Multiply 4 times 2.

$$8x^{4-1}$$

Subtract 1 from 4.

$$8x^{3}$$

Differentiate w.r.t. x

$$24x^{2}$$