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1.2 Übungen

Aus Online Mathematik Brückenkurs 2

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Version vom 12:25, 10. Mär. 2009

       Theory          Examples      

Example 1.2:1

Calculate the derivative of the following functions and write the answer in simplest possible form:

a) cosxsinx b) x2lnx c) x+1x2+1
d) xsinx e) xlnx f) sinxxlnx

Example 1.2:2

Calculate the derivative of the following functions and write the answer in simplest possible form:

a) sinx2 b) ex2+x c) cosx 
d) lnlnx e) x(2x+1)4 f) cos1x 

Example 1.2:3

Calculate the derivative of the following functions and write the answer in simplest possible form:

a) ln(x+x+1)  b) x1x+1  c) 1x1x2
d) sincossinx e) \displaystyle e^{\sin x^2} f) \displaystyle x^{\tan x}

Example 1.2:4

Calculate the second derivative of the following functions and write the answer in simplest possible form:

a) \displaystyle \displaystyle\frac{x}{\sqrt{1-x^2}} b) \displaystyle x ( \sin \ln x +\cos \ln x )