Solve m^6*m^13/m^17e

$$\frac { m ^ { 6 } \cdot m ^ { 13 } } { m ^ { 17 } } e$$

Evaluate

$$em^{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 13 to get 19.

$$\frac{m^{19}}{m^{17}}e$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 17 from 19 to get 2.

$$m^{2}e$$

Differentiate w.r.t. m

$$2em$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 13 to get 19.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m^{19}}{m^{17}}e)$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 17 from 19 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{2}e)$$

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

$$2em^{2-1}$$

Subtract 1 from 2.

$$2em^{1}$$

For any term t, t^{1}=t.

$$2em$$