Solve 8x^5(3x)

$$8 x ^ { 5 } ( 3 x )$$

Evaluate

$$24x^{6}$$

Solution Steps

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

$$8x^{6}\times 3$$

Multiply 8 and 3 to get 24.

$$24x^{6}$$

Differentiate w.r.t. x

$$144x^{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{6}\times 3)$$

Multiply 8 and 3 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(24x^{6})$$

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

$$6\times 24x^{6-1}$$

Multiply 6 times 24.

$$144x^{6-1}$$

Subtract 1 from 6.

$$144x^{5}$$