Solve (f*g)(3/(sqrt{x-3)^2-10})

$$( f \cdot g ) ( \frac { 3 } { ( \sqrt { x - 3 } ) ^ { 2 } - 10 } )$$

Evaluate

$$\frac{3fg}{x-13}$$

Solution Steps

Calculate \sqrt{x-3} to the power of 2 and get x-3.

$$fg\times \frac{3}{x-3-10}$$

Subtract 10 from -3 to get -13.

$$fg\times \frac{3}{x-13}$$

Express f\times \frac{3}{x-13} as a single fraction.

$$\frac{f\times 3}{x-13}g$$

Express \frac{f\times 3}{x-13}g as a single fraction.

$$\frac{f\times 3g}{x-13}$$

Differentiate w.r.t. x

$$-\frac{3fg}{\left(x-13\right)^{2}}$$