Solve 4/3+R/12+4R

$$\frac { \frac { 4 } { 3 + R } } { 12 + 4 R }$$

Evaluate

$$\frac{1}{\left(R+3\right)^{2}}$$

Solution Steps

Express \frac{\frac{4}{3+R}}{12+4R} as a single fraction.

$$\frac{4}{\left(3+R\right)\left(12+4R\right)}$$

Apply the distributive property by multiplying each term of 3+R by each term of 12+4R.

$$\frac{4}{36+12R+12R+4R^{2}}$$

Combine 12R and 12R to get 24R.

$$\frac{4}{36+24R+4R^{2}}$$

Differentiate w.r.t. R

$$-\frac{2}{\left(R+3\right)^{3}}$$