Solve g(x)=2x/x+5quadD:quadg(1/2)=

$$g ( x ) = \frac { 2 x } { x + 5 } \quad D : \quad g ( \frac { 1 } { 2 } ) =$$

Evaluate

$$\frac{Dx}{g\left(x+5\right)}$$

Short Solution Steps

Express \frac{2x}{x+5}D as a single fraction.

$$\frac{\frac{2xD}{x+5}}{g}\times \frac{1}{2}$$

Express \frac{\frac{2xD}{x+5}}{g} as a single fraction.

$$\frac{2xD}{\left(x+5\right)g}\times \frac{1}{2}$$

Multiply \frac{2xD}{\left(x+5\right)g} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2xD}{\left(x+5\right)g\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{Dx}{g\left(x+5\right)}$$

Use the distributive property to multiply g by x+5.

$$\frac{Dx}{gx+5g}$$

Differentiate w.r.t. x

$$\frac{5D}{g\left(x+5\right)^{2}}$$