Question

9. et + In x
10. 2* + In x
Find the derivatives of the following (11-25)
11. et + 2
12. log5x + 5 sin x
13. ex In x
14. 2*(x + sin x)
15. etano
16. ex/x+ sec x
17. (x + 5tan x) In x
18. x5/2 a' + In x
19. + cot x
20. Vcot-le
In x
et
21. 3*e*+
ex
22. x2(e X+ log101)
In x
23. (e-*cos x + In c)/(10% + log10x)
24. In ln ln(x2)
25. In(tan-? 31,​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

$f(x) = x ^{2} - 2 \\ f(x + h) = (x + h)^{2} - 2 \\ Now, \\ \\ f'(x)= \frac{f(x + h) - f(x)}{h} \\ \displaystyle \lim_{h \to 0} = \frac{(x + h)^{2} - 2 - (x^{2} - 2)}{h} \\ \displaystyle \lim_{h \to 0} = \frac{x ^{2} + h^{2} + 2xh-2 - x^{2} + 2}{h} \\\displaystyle \lim_{h \to 0} = \frac{\cancel{x ^{2}} + h ^{2} + 2xh \: \cancel{ -2} \: \: \: \cancel{-x^{2}} \: \cancel { + 2}}{h} \\ \displaystyle \lim_{h \to 0} = \frac{h^{2} + 2xh }{h} \\\displaystyle \lim_{h \to 0} = h + 2x \\ = 0 + 2x \\ = 2x$

f'(x) = 2x

f'(10) = 2*10

‎‎‎‎‎‎ ‎ ‎ ‎‎ ‎ ‎ ‎‎ ‎ ‎=20

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