Question

find the derivative of y=sqrt(11x+(sqrt(11x+(sqrt11x)))

Answer 1

$$g(x)=\sqrt{11+x}\\g'(x)=\frac1{2\sqrt{11+x}}$$right?

Answer 2

Now recognize \(y=g(g(11x))\)

Answer 3

oops, \(y=g(g(\sqrt{11x}))\)

Answer 4

so now use the chain rule:$$y'=\frac{dg}{dx}\cdot\frac{dg}{dx}\cdot\frac{d}{dx}[\sqrt{11x}]=\left(\frac1{2\sqrt{11+x}}\right)^2\left(\frac{\sqrt{11}}{2\sqrt{x}}\right)$$

Answer 5

can you simplify?

Answer 6

1/2(11x+sqrt(11x+sqrt11x)^-1/2(11+1/2(11x+sqrt11x)(11+1/2sqrt11/x

Answer 7

erm

Answer 8

\[\large y' = \left(\frac{1}{2 \sqrt{11+x}}\right)^2 \cdot \left(\frac{\sqrt{11}}{2\sqrt{x}}\right)\] distribute the 2 into both numerator and denominator. \[\large y' = \left(\frac{1^2}{2^2\cdot(\sqrt{11+x})^2}\right)\cdot \left(\frac{\sqrt{11}}{2\sqrt{x}}\right)\]\[\large y' = \frac{1}{4(11+x)}\cdot \frac{\sqrt{11}}{2\sqrt{x}}\] Can you simplify this now?...

Answer 9

no