Solve 14t^242t^3

$$14 t ^ { 2 } 42 t ^ { 3 }$$

Evaluate

$$588t^{5}$$

Solution Steps

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

$$14t^{5}\times 42$$

Multiply 14 and 42 to get 588.

$$588t^{5}$$

Differentiate w.r.t. t

$$2940t^{4}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}t}(14t^{5}\times 42)$$

Multiply 14 and 42 to get 588.

$$\frac{\mathrm{d}}{\mathrm{d}t}(588t^{5})$$

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

$$5\times 588t^{5-1}$$

Multiply 5 times 588.

$$2940t^{5-1}$$

Subtract 1 from 5.

$$2940t^{4}$$