Solve (2^2x^2)*2

$$( 2 ^ { 2 } x ^ { 2 } ) \times 2$$

Evaluate

$$8x^{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$2^{3}x^{2}$$

Calculate 2 to the power of 3 and get 8.

$$8x^{2}$$

Differentiate w.r.t. x

$$16x$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2^{3}x^{2})$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{2})$$

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

$$2\times 8x^{2-1}$$

Multiply 2 times 8.

$$16x^{2-1}$$

Subtract 1 from 2.

$$16x^{1}$$

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

$$16x$$