Solve w^14/w^7*w^15/w^5

$$\frac { w ^ { 14 } } { w ^ { 7 } } \cdot \frac { w ^ { 15 } } { w ^ { 5 } }$$

Evaluate

$$w^{17}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 14 to get 7.

$$w^{7}\times \frac{w^{15}}{w^{5}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 15 to get 10.

$$w^{7}w^{10}$$

To multiply powers of the same base, add their exponents. Add 7 and 10 to get 17.

$$w^{17}$$

Differentiate w.r.t. w

$$17w^{16}$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 14 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}w}(w^{7}\times \frac{w^{15}}{w^{5}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 15 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}w}(w^{7}w^{10})$$

To multiply powers of the same base, add their exponents. Add 7 and 10 to get 17.

$$\frac{\mathrm{d}}{\mathrm{d}w}(w^{17})$$

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

$$17w^{17-1}$$

Subtract 1 from 17.

$$17w^{16}$$