Answer to Question #331661 in Calculus for Olga

Question

Find the derivative of

F(x)=14+ln  x /√ x + 5

a. 3x+10 / 2 x (x + 5)

b. x +10 / 2x (x + 5)

c. 10 / 2x ( x + 5)

d. 2x (x + 5)

Answer 1

$F(x)=14+\frac{ln(x)}{\sqrt{x+5}}$

$F'(x)=\frac{(ln(x)'\sqrt{x+5}-(\sqrt{x+5})'ln(x)}{x+5}+0=\frac{\sqrt{x+5}/x- ln(x)/(2\sqrt{x+5})}{x+5}=\frac{1}{x\sqrt{x+5}}-\frac{ln(x)}{2(x+5)^{3/2}}$