Solve (7x^5)(8x)

$$( 7 x ^ { 5 } ) ( 8 x )$$

Evaluate

$$56x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$7x^{6}\times 8$$

Multiply 7 and 8 to get 56.

$$56x^{6}$$

Differentiate w.r.t. x

$$336x^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{6}\times 8)$$

Multiply 7 and 8 to get 56.

$$\frac{\mathrm{d}}{\mathrm{d}x}(56x^{6})$$

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

$$6\times 56x^{6-1}$$

Multiply 6 times 56.

$$336x^{6-1}$$

Subtract 1 from 6.

$$336x^{5}$$