Solve 2x^6(2x)

$$2 x ^ { 6 } ( 2 x )$$

Evaluate

$$4x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$2x^{7}\times 2$$

Multiply 2 and 2 to get 4.

$$4x^{7}$$

Differentiate w.r.t. x

$$28x^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{7}\times 2)$$

Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{7})$$

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

$$7\times 4x^{7-1}$$

Multiply 7 times 4.

$$28x^{7-1}$$

Subtract 1 from 7.

$$28x^{6}$$