Log Integration - Differ hence find TYS 1

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Logarithms - Integration - Differentiate ... hence find problems.
Test Yourself 1.

Logarithms.	1. (i) Differentiate y = (ln x)². (ii) Hence evaluate . Answer.Integral = 0.5.
	2. (i) If , show that (ii) Hence or otherwise evaluate Answer.Integral = (ln3)/2.
	3. (i) Show that . (ii) Hence evaluate . Answer.Integral = 1.
	4. Differentiate log_e (log_e x) and hence evaluate . Answer.Integral = log_e 2.
	5. (i) Find the derivative of log_e (x² - 1). (ii) Hence or otherwise find . Answer.Integral = 4log_e (8/3).
	6. Given that , evaluate giving your answer to 4 significant figures. Answer.Integral = 30.98.
	7. Find the value of by first differentiating y = x log_e x. Answer.Integral = 0.
	8. (i) Find the derivative of (log_e 6x)³ (ii) Hence evaluate . Answer correct to 1 decimal place. Answer.Integral = 5.1.
	9. (i) Show that (ii) Hence evaluate .
	10. (i) Differentiate e^x + e^-x (ii) Hence find .