Solve 8w^20w^38w^62

$$8 w ^ { 20 } w ^ { 38 } w ^ { 62 }$$

Evaluate

$$8w^{120}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 20 and 38 to get 58.

$$8w^{58}w^{62}$$

To multiply powers of the same base, add their exponents. Add 58 and 62 to get 120.

$$8w^{120}$$

Differentiate w.r.t. w

$$960w^{119}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 20 and 38 to get 58.

$$\frac{\mathrm{d}}{\mathrm{d}w}(8w^{58}w^{62})$$

To multiply powers of the same base, add their exponents. Add 58 and 62 to get 120.

$$\frac{\mathrm{d}}{\mathrm{d}w}(8w^{120})$$

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

$$120\times 8w^{120-1}$$

Multiply 120 times 8.

$$960w^{120-1}$$

Subtract 1 from 120.

$$960w^{119}$$