Solve 3v^-1w^0/3v^-2w

$$\frac { 3 v ^ { - 1 } w ^ { 0 } } { 3 v ^ { - 2 } w }$$

Evaluate

$$\frac{v}{w}$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{1}{v}w^{0}}{v^{-2}w}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{v^{1}w^{0}}{w}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{v^{1}}{w^{1}}$$

Calculate v to the power of 1 and get v.

$$\frac{v}{w^{1}}$$

Calculate w to the power of 1 and get w.

$$\frac{v}{w}$$

Differentiate w.r.t. v

$$\frac{1}{w}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{3w^{0}}{3w}v^{-1-\left(-2\right)})$$

Do the arithmetic.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$\frac{1}{w}v^{1-1}$$

Do the arithmetic.

$$\frac{1}{w}v^{0}$$

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

$$\frac{1}{w}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{w}$$