Solve 14t^242t^5

$$14 t ^ { 2 } 42 t ^ { 5 }$$

Evaluate

$$588t^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$14t^{7}\times 42$$

Multiply 14 and 42 to get 588.

$$588t^{7}$$

Differentiate w.r.t. t

$$4116t^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}t}(14t^{7}\times 42)$$

Multiply 14 and 42 to get 588.

$$\frac{\mathrm{d}}{\mathrm{d}t}(588t^{7})$$

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

$$7\times 588t^{7-1}$$

Multiply 7 times 588.

$$4116t^{7-1}$$

Subtract 1 from 7.

$$4116t^{6}$$