Solve (w*w^6)div(w^5xw^2)

$$( w \times w ^ { 6 } ) \div ( w ^ { 5 } x w ^ { 2 } )$$

Evaluate

$$\frac{1}{x}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\frac{w^{7}}{w^{5}xw^{2}}$$

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

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

Cancel out w^{7} in both numerator and denominator.

$$\frac{1}{x}$$

Differentiate w.r.t. x

$$-\frac{1}{x^{2}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{w^{7}}{w^{5}xw^{2}})$$

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

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

Cancel out w^{7} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x})$$

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

$$-x^{-1-1}$$

Subtract 1 from -1.

$$-x^{-2}$$