Question #331661

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)


1
Expert's answer
2022-04-28T05:20:56-0400

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

F(x)=(ln(x)x+5(x+5)ln(x)x+5+0=x+5/xln(x)/(2x+5)x+5=1xx+5ln(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}}


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