Solve 2m/2-m

$$\frac { 2 m } { 2 - m }$$

Differentiate w.r.t. m

$$\frac{4}{\left(m-2\right)^{2}}$$

Steps Using Derivative Rule for Quotient

For any two differentiable functions, the derivative of the quotient of two functions is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the denominator squared.

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

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}.

$$\frac{\left(-m^{1}+2\right)\times 2m^{1-1}-2m^{1}\left(-1\right)m^{1-1}}{\left(-m^{1}+2\right)^{2}}$$

Do the arithmetic.

$$\frac{\left(-m^{1}+2\right)\times 2m^{0}-2m^{1}\left(-1\right)m^{0}}{\left(-m^{1}+2\right)^{2}}$$

Expand using distributive property.

$$\frac{-m^{1}\times 2m^{0}+2\times 2m^{0}-2m^{1}\left(-1\right)m^{0}}{\left(-m^{1}+2\right)^{2}}$$

To multiply powers of the same base, add their exponents.

$$\frac{-2m^{1}+2\times 2m^{0}-2\left(-1\right)m^{1}}{\left(-m^{1}+2\right)^{2}}$$

Do the arithmetic.

$$\frac{-2m^{1}+4m^{0}-\left(-2m^{1}\right)}{\left(-m^{1}+2\right)^{2}}$$

Combine like terms.

$$\frac{\left(-2-\left(-2\right)\right)m^{1}+4m^{0}}{\left(-m^{1}+2\right)^{2}}$$

Subtract -2 from -2.

$$\frac{4m^{0}}{\left(-m^{1}+2\right)^{2}}$$

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

$$\frac{4m^{0}}{\left(-m+2\right)^{2}}$$

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

$$\frac{4\times 1}{\left(-m+2\right)^{2}}$$

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

$$\frac{4}{\left(-m+2\right)^{2}}$$

Evaluate

$$\frac{2m}{2-m}$$