Solve 16x^2*2x^2=

$$16 x ^ { 2 } \times 2 x ^ { 2 } =$$

Evaluate

$$32x^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$16x^{4}\times 2$$

Multiply 16 and 2 to get 32.

$$32x^{4}$$

Differentiate w.r.t. x

$$128x^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16x^{4}\times 2)$$

Multiply 16 and 2 to get 32.

$$\frac{\mathrm{d}}{\mathrm{d}x}(32x^{4})$$

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

$$4\times 32x^{4-1}$$

Multiply 4 times 32.

$$128x^{4-1}$$

Subtract 1 from 4.

$$128x^{3}$$