Solve (4x^3)(x^2)(4x)

$$( 4 x ^ { 3 } ) ( x ^ { 2 } ) ( 4 x )$$

Evaluate

$$16x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$4x^{5}\times 4x$$

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

$$4x^{6}\times 4$$

Multiply 4 and 4 to get 16.

$$16x^{6}$$

Differentiate w.r.t. x

$$96x^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{5}\times 4x)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{6}\times 4)$$

Multiply 4 and 4 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16x^{6})$$

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

$$6\times 16x^{6-1}$$

Multiply 6 times 16.

$$96x^{6-1}$$

Subtract 1 from 6.

$$96x^{5}$$