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1.2 Übungen

(Unterschied zwischen Versionen)

Version vom 13:41, 10. Mär. 2009

Beispiels

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

a)	\displaystyle \cos x \cdot \sin x	b)	\displaystyle x^2\ln x	c)	\displaystyle \displaystyle\frac{x^2+1}{x+1}
d)	\displaystyle \displaystyle\frac{\sin x}{x}	e)	\displaystyle \displaystyle\frac{x}{\ln x}	f)	\displaystyle \displaystyle\frac{x \ln x}{\sin x}

Antwort

Lösung a

Lösung b

Lösung c

Lösung d

Lösung e

Lösung f

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

a)	\displaystyle \sin x^2	b)	\displaystyle e^{x^2+x}	c)	\displaystyle \sqrt{\cos x}
d)	\displaystyle \ln \ln x	e)	\displaystyle x(2x+1)^4	f)	\displaystyle \cos \sqrt{1-x}

Antwort

Lösung a

Lösung b

Lösung c

Lösung d

Lösung e

Lösung f

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

a)	\displaystyle \ln (\sqrt{x} + \sqrt{x+1}\,)	b)	\displaystyle \sqrt{\displaystyle \frac{x+1}{x-1}}	c)	\displaystyle \displaystyle\frac{1}{x\sqrt{1-x^2}}
d)	\displaystyle \sin \cos \sin x	e)	\displaystyle e^{\sin x^2}	f)	\displaystyle x^{\tan x}