Solve 2x^4*2x^4

$$2 x ^ { 4 } \cdot 2 x ^ { 4 }$$

Evaluate

$$4x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

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

Multiply 2 and 2 to get 4.

$$4x^{8}$$

Differentiate w.r.t. x

$$32x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

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

Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{8})$$

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

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

Multiply 8 times 4.

$$32x^{8-1}$$

Subtract 1 from 8.

$$32x^{7}$$