Solve 12x^7*2x

$$12 x ^ { 7 } \times 2 x$$

Evaluate

$$24x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$12x^{8}\times 2$$

Multiply 12 and 2 to get 24.

$$24x^{8}$$

Differentiate w.r.t. x

$$192x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{8}\times 2)$$

Multiply 12 and 2 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(24x^{8})$$

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

$$8\times 24x^{8-1}$$

Multiply 8 times 24.

$$192x^{8-1}$$

Subtract 1 from 8.

$$192x^{7}$$