Solve 2w^2div4w^5

$$2 w ^ { 2 } \div 4 w ^ { 5 }$$

Evaluate

$$\frac{w^{7}}{2}$$

Solution Steps

Divide 2w^{2} by 4 to get \frac{1}{2}w^{2}.

$$\frac{1}{2}w^{2}w^{5}$$

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

$$\frac{1}{2}w^{7}$$

Differentiate w.r.t. w

$$\frac{7w^{6}}{2}$$

Steps Using Definition of a Derivative

Divide 2w^{2} by 4 to get \frac{1}{2}w^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{1}{2}w^{2}w^{5})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{1}{2}w^{7})$$

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

$$7\times \frac{1}{2}w^{7-1}$$

Multiply 7 times \frac{1}{2}.

$$\frac{7}{2}w^{7-1}$$

Subtract 1 from 7.

$$\frac{7}{2}w^{6}$$