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)
F(x)=14+ln(x)x+5F(x)=14+\frac{ln(x)}{\sqrt{x+5}}F(x)=14+x+5ln(x)
F′(x)=(ln(x)′x+5−(x+5)′ln(x)x+5+0=x+5/x−ln(x)/(2x+5)x+5=1xx+5−ln(x)2(x+5)3/2F'(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}}F′(x)=x+5(ln(x)′x+5−(x+5)′ln(x)+0=x+5x+5/x−ln(x)/(2x+5)=xx+51−2(x+5)3/2ln(x)
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