Solve (2t^3)(3t^2)(4t)=

$$( 2 t ^ { 3 } ) ( 3 t ^ { 2 } ) ( 4 t ) =$$

Evaluate

$$24t^{6}$$

Solution Steps

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

$$2t^{5}\times 3\times 4t$$

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

$$2t^{6}\times 3\times 4$$

Multiply 2 and 3 to get 6.

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

Multiply 6 and 4 to get 24.

$$24t^{6}$$

Differentiate w.r.t. t

$$144t^{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}t}(2t^{5}\times 3\times 4t)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}t}(2t^{6}\times 3\times 4)$$

Multiply 2 and 3 to get 6.

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

Multiply 6 and 4 to get 24.

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

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

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

Multiply 6 times 24.

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

Subtract 1 from 6.

$$144t^{5}$$