Solve v^0/v^2

$$\frac { v ^ { 0 } } { v ^ { 2 } }$$

Evaluate

$$\frac{1}{v^{2}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{v^{0}}{v^{2}}$$

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

$$v^{-2}$$

Differentiate w.r.t. v

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

Steps Using Chain Rule

Rewrite v^{2} as v^{0}v^{2}. Cancel out v^{0} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{1}{v^{2}})$$

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

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

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}.

$$-\left(v^{2}\right)^{-2}\times 2v^{2-1}$$

Simplify.

$$-2v^{1}\left(v^{2}\right)^{-2}$$

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

$$-2v\left(v^{2}\right)^{-2}$$