Solve 12s^37s^4

$$12 s ^ { 3 } 7 s ^ { 4 }$$

Evaluate

$$84s^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$12s^{7}\times 7$$

Multiply 12 and 7 to get 84.

$$84s^{7}$$

Differentiate w.r.t. s

$$588s^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}s}(12s^{7}\times 7)$$

Multiply 12 and 7 to get 84.

$$\frac{\mathrm{d}}{\mathrm{d}s}(84s^{7})$$

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

$$7\times 84s^{7-1}$$

Multiply 7 times 84.

$$588s^{7-1}$$

Subtract 1 from 7.

$$588s^{6}$$