Solve 3w^-3*2w^6

$$3 w ^ { - 3 } \times 2 w ^ { 6 }$$

Evaluate

$$6w^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and 6 to get 3.

$$3w^{3}\times 2$$

Multiply 3 and 2 to get 6.

$$6w^{3}$$

Differentiate w.r.t. w

$$18w^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -3 and 6 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}w}(3w^{3}\times 2)$$

Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}w}(6w^{3})$$

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

$$3\times 6w^{3-1}$$

Multiply 3 times 6.

$$18w^{3-1}$$

Subtract 1 from 3.

$$18w^{2}$$