Solve v^7divv^4divv^2

$$v ^ { 7 } \div v ^ { 4 } \div v ^ { 2 }$$

Evaluate

$$v$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 7 to get 3.

$$\frac{v^{3}}{v^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 3 to get 1.

$$v^{1}$$

Calculate v to the power of 1 and get v.

$$v$$

Differentiate w.r.t. v

$$1$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 7 to get 3.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 3 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}v}(v^{1})$$

Calculate v to the power of 1 and get v.

$$\frac{\mathrm{d}}{\mathrm{d}v}(v)$$

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

$$v^{1-1}$$

Subtract 1 from 1.

$$v^{0}$$

For any term t except 0, t^{0}=1.

$$1$$