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emmasim [6.3K]
3 years ago
13

How do you find the derivative of y=ln(cos(x))y=ln(cos(x)) ?

Mathematics
1 answer:
makkiz [27]3 years ago
7 0
y=ln(cosx)\\\\We\ know:\\(lnx)'=\frac{1}{x}\ and\ (cosx)'=-sinx\ and\ \{f[g(x)]\}'=f'[g(x)]\cdot g'(x)\\\\therefore:\\\\y'=\frac{1}{cosx}\cdot(-sinx)=-\frac{sinx}{cosx}=-tanx
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Use the discriminant to find the number and type of solution for x^2+6x=-9​
likoan [24]

Answer:

D = 0; one real root

Step-by-step explanation:

Discriminant Formula:

\displaystyle \large{D =  {b}^{2}  - 4ac}

First, arrange the expression or equation in ax^2+bx+c = 0.

\displaystyle \large{ {x}^{2}  + 6x =  - 9}

Add both sides by 9.

\displaystyle \large{ {x}^{2}  + 6x + 9 =  - 9 + 9} \\  \displaystyle \large{ {x}^{2}  + 6x + 9 =  0}

Compare the coefficients so we can substitute in the formula.

\displaystyle \large{a {x}^{2}  + bx + c =  {x}^{2}  + 6x + 9 }

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Substitute a = 1, b = 6 and c = 9 in the formula.

\displaystyle \large{D =  {6}^{2}  - 4(1)(9)} \\  \displaystyle \large{D =  36 - 36} \\  \displaystyle \large{D =  0}

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6 0
2 years ago
PLEASE HELP ASAP 25 PTS TO RIGHT/BEST ANSWER
Novay_Z [31]
Subtract 1111 from both sides

5{e}^{{4}^{x}}=22-115e​4​x​​​​=22−11


 

Simplify 22-1122−11 to 1111

5{e}^{{4}^{x}}=115e​4​x​​​​=11



 

Divide both sides by 55

{e}^{{4}^{x}}=\frac{11}{5}e​4​x​​​​=​5​​11​​



 

Use Definition of Natural Logarithm: {e}^{y}=xe​y​​=x if and only if \ln{x}=ylnx=y

{4}^{x}=\ln{\frac{11}{5}}4​x​​=ln​5​​11​​



 

: {b}^{a}=xb​a​​=x if and only if log_b(x)=alog​b​​(x)=a

x=\log_{4}{\ln{\frac{11}{5}}}x=log​4​​ln​5​​11​​



 

Use Change of Base Rule: \log_{b}{x}=\frac{\log_{a}{x}}{\log_{a}{b}}log​b​​x=​log​a​​b​​log​a​​x​​

x=\frac{\log{\ln{\frac{11}{5}}}}{\log{4}}x=​log4​​logln​5​​11​​​​



 

Use Power Rule: \log_{b}{{x}^{c}}=c\log_{b}{x}log​b​​x​c​​=clog​b​​x
\log{4}log4 -> \log{{2}^{2}}log2​2​​ -> 2\log{2}2log2

x=\frac{\log{\ln{\frac{11}{5}}}}{2\log{2}}x=​2log2​


Answer= −0.171
7 0
3 years ago
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