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Find the derivative of the following via implicit differentiation:
d/dx(h(x)) = d/dx(sqrt(e^x))
The derivative of h(x) is h'(x):
h'(x) = d/dx(sqrt(e^x))
Using the chain rule, d/dx(sqrt(e^x)) = ( dsqrt(u))/( du) ( du)/( dx), where u = e^x and ( d)/( du)(sqrt(u)) = 1/(2 sqrt(u)):
h'(x) = (d/dx(e^x))/(2 sqrt(e^x))
The derivative of e^x is e^x:
h'(x) = e^x/(2 sqrt(e^x))
Simplify the expression:
h'(x) = sqrt(e^x)/2
Expand the left hand side:
Answer: |  h'(x) = sqrt(e^x)/2

How do u put this in slope form

(10,33) (5,15)

ex: y=mx+b

\(\text{Point 1: } ( x_1 = 10,\ y_1 = 33) \\ \text{Point 2: }(x_2 = 5,\ y_2 = 15 )\)

\(\begin{array}{rcll} m &=& \frac{y_2-y_1}{x_2-x_1} \\\\ m &=& \frac{15-33}{5-10} \\\\ m &=& \frac{-18}{-5} \\\\ m &=& \frac{18}{5} \\\\ \mathbf{m} &\mathbf{=}& \mathbf{3.6} \\\\ \hline \\ \frac{y-y_1}{x-x_1} &=& m\\\\ \frac{y-33}{x-10} &=& 3.6 \qquad & | \qquad \cdot (x-10) \\\\ y-33 &=& 3.6\cdot( x-10 ) \qquad & | \qquad +33 \\\\ y &=& 3.6\cdot( x-10 ) +33 \\\\ y &=& 3.6\cdot x -3.6\cdot 10 +33 \\\\ y &=& 3.6\cdot x -36 +33 \\\\ \mathbf{y} &\mathbf{=}& \mathbf{ 3.6\cdot x -3 } \end{array}\)

Hey! A55H0LE! Yeah, you, guest. Go .F**k. yourself.

You got it all wrong except for my p***s being really fat and long, but I dont f**k your mom neither suck my own d**k I f**k MEgan Fox and Nicolle Aninston and they suck my d**k!!! JELOUS !!!!!

F**k you n***a you suck your own fat a*s d**k. you r***d my momma and her name is crocodile and you use her as a s*x slave and you still fucking love her

I do his name is Nate and my other friend Man-Man they were doing it together in the boys stall and with Man-Man's teddy bear too!!!

A worker is paid 0.05 on the first day, 0.10 on the second day, 0.20 on the third day and 0.40 on the fourth day, and so on. How much money in total does the work earn after working 21 days?

\(\small{ \begin{array}{llll} \text{after } 1 \text{ day }:& 0.05 \\ \text{after } 2 \text{ days }: & 0.10 &=& 0.05 \cdot 2 \\ \text{after } 3 \text{ days }: & 0.20 = 0.10\cdot 2 = 0.05 \cdot 2 \cdot 2 &=& 0.05 \cdot 2^2\\ \text{after } 4 \text{ days }: & 0.40 = 0.20\cdot 2 =0.05 \cdot 2^2 \cdot 2 \cdot 2 &=& 0.05 \cdot 2^3\\ \dots \\ \text{after } 21 \text{ days }:&&& 0.05 \cdot 2^{21-1}\\ &&& = 0.05 \cdot 2^{20} = 0.05\cdot 1048576 = 52428.80\\ \end{array} }\)

He earn after 21 days 52428.80

Thank you so much!

                   x

Lim           _____   = ?

                    x2-1

x→(infinity sign)

\(\begin{array}{rcll} \lim \limits_{x\to \infty} { \left( \dfrac{x } { x^2-1 } \right) } &=& \lim \limits_{x\to \infty} { \left( \dfrac{ x } { x^2-1 } \frac{:x^2}{:x^2} \right) } \\ &=& \lim \limits_{x\to \infty} { \left( \dfrac{ \frac{x}{x^2} } { \frac{x^2-1}{x^2} } \right) } \\ &=& \lim \limits_{x\to \infty} { \left( \dfrac{ \frac{x}{x^2} } { \frac{x^2}{x^2} - \frac{1}{x^2} } \right) } \\ &=& \lim \limits_{x\to \infty} { \left( \dfrac{ \frac{1}{x} } { 1 - \frac{1}{x^2} } \right) } \\ &=& \dfrac{ 0 } { 1 - 0 } \\ &=& \dfrac{ 0 } { 1 } \\ \lim \limits_{x\to \infty} { \left( \dfrac{x } { x^2-1 } \right) } &=& 0 \\ \end{array}\)

Ok. Thanks. What is Bruce Wayne talking about?

You are jumping on a trampoline. Your height y (in feet) above the trampoline after t seconds can be represented by y=-16t^2+24t. How many seconds are you in the air?

\(\begin{array}{rcll} y&=&-16t^2+24t \qquad y(t) = 0\\ -16t^2+24t &=& 0 \\ t(\underbrace{-16\cdot t + 24}_{=0} ) &=& 0 \\\\ -16\cdot t + 24 &=& 0 \\ -16\cdot t + 24 &=& \qquad & | \qquad -24\\ -16\cdot t &=& - 24 \qquad & | \qquad : (-16)\\ t &=& \frac{-24}{-16} \\ t &=& \frac{24}{16} \\ t &=& \frac{3}{2} \\ t &=& 1.5\ \text{seconds} \\ \end{array}\)

Yaya Toure is so awesome. He used to play for Barca, but now he is with Man C. His free kicks are way better than Beckham's.

How to find percent of discount

regular price: $42

Sale price: $36

\(\begin{array}{rcll} $36 &=& $42 \cdot ( 100\ \% - x ) \qquad & | \qquad : $42\\ \frac{$36} {$42} &=& 100\ \% - x \\ \frac{36} {42} &=& 100\ \% - x \qquad & | \qquad +x\\ x + \frac{36} {42} &=& 100\ \% \qquad & | \qquad - \frac{36} {42}\\ x &=& 100\ \% - \frac{36} {42} \qquad & | \qquad 100\ \% = 1\\ x &=& 1 - \frac{36} {42} \\ x &=& 1 - \frac{18} {21} \\ x &=& \frac{21 -18} {21} \\ x &=& \frac{3} {21} \\ x &=& \frac{1} {7} \\ x &=& 0.14285714286\\ \mathbf{ x } & \mathbf{=} & \mathbf{ 14.285714286 \ \% } \end{array}\)

The discount is 14.29 %

How does that work? I got 3

what your saying doesnt really makes sense Bruce....

In prabability.....we can only find the probability of the occurance of the event based on its earlier outcomes......in this question they asked "whats the probability of getting 1" and in the outcomes....1 was occuring twice.....so its probility would be 2 out of 9.i.e.the total number of outcomes....

i thought you were serious about this question you know,.......

4 

Wow. I don't know any idiot that stuck his d**k in a pencil sharpener

It really depends on what you're trying to figure out

4/12 (BTW this is not simpilfyed)

Divide

99*2=198

Trust this ! 

1611/4370

\(\frac{1611}{4370} = 0.36864988558\)

Actully.....

it doesn't matter what you got its what you hope to its really...

1/9

you rolled it 9 times and wan't 1 

hope you learned somthing new lol