Exponentials

/Tag: Exponentials
5 06, 2017

Challenging Exponentials

By |2017-06-05T10:50:34+10:00June 5th, 2017|Tags: , , |0 Comments

Challenging Exponentials Find the derivative of $$y=x^x$$. let $$y = {\left( {{e^{\ln x}}} \right)^x}$$ as eln x = x $$y = {e^{x.\ln x}}$$ let y = eu consider separately u = x.ln x $$\frac{du}{dx}=\ln x . 1 + x.\frac{1}{x}$$ $$\frac{du}{dx}=\ln x +1$$ to differentiate y = eu, differentiate [...]

10 08, 2015

Exam Style Questions

By |2016-11-03T10:02:17+10:00August 10th, 2015|Tags: , , , , , |0 Comments

Exam Style Questions The following is a table of values for the function $$y = \frac{2}{{x(x + 1)}}$$. a. Using the information in the table and Simpson's Rule with five function values, find an approximation for $$\int\limits_1^5 {\frac{2}{{x(x + 1)}}dx} $$ correct to 3 decimal places. b. Prove that $$\frac{2}{{x(x + 1)}} [...]

10 08, 2015

Integrating e & Log

By |2016-11-03T09:48:06+10:00August 10th, 2015|Tags: , , , , , , |0 Comments

Integrating e & Log worked examples Find the primitive of:  $$\frac{1-xe^x}{x}$$. $$\frac{1-xe^x}{x}=\frac1x-\frac{xe^x}{x}$$ split into two separate fractions to make simplifying a little easier $$=\frac1x-e^x$$ simplify  y = ln x - ex + c find the primitive (integral), remembering that $$\int \frac1x\,dx=ln x+c$$ amd $$\int e^x dx = e^x+c$$ [...]

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