Answer to Question #207349 in Calculus for Paballo

Question

Find the derivative of the fun

tion

f(x) = 15 − x

√

6x + 1 +

x

1 + x

.

[1℄ − √

9x+1

6x+1 +

1

(1+x)

2

[2℄ − √

3x

6x+1 +

√

6x + 1 + 1

(1+x)

2

[3℄ √

3x

6x+1 + 1

(1+x)

2

[4℄ √

9x+1

6x+1 +

1−2x

(1+x)

2

Answer 1

Solution.

$f(x)=15-x\sqrt{6x+1}+x(1+x)$

Then$f'(x)=-\sqrt{6x+1}-\frac{6x}{2\sqrt{6x+1}}+1+x+x=\newline -\sqrt{6x+1}-\frac{3x}{\sqrt{6x+1}}+1+2x.$