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Logarithmic function: Calculus help?
Find the derivative of the function... These are the last few questions on my homework that i didn't understand. Any help will be great thank you.
1. y= t ln sqrt t
2. y= ln x/1+ln x
3. y = theta sin (ln theta)
2 Answers
- ?Lv 79 years ago
1) y = t ln (√t)
y = t (1/2) ln t = 1/2 t ln t
dy/dt = (1/2) d/dt [ t ] * ln (t )+ t d/dt [ ln (t) ] Product rule
dy/dt = (1/2)(1 * ln (t) + t (1/t ))
dy/dt = (1/2) (ln (t) + 1)
2) y = ln (x ) /( 1 + ln x) Parentheses matter
dy/dx = ( d/dx [ ln (x)] * (1 + ln x) - ln (x) * d/dx [1 + ln x] ) / (1 + ln x)^2
Quotient Rule
dy/dx = ( (1/x)(1 + ln x) - ln x (1/x)) / ((1 + ln x)^2
dy/dx = (1/x) / (1 + ln x)^2
dy/dx = / (x (1 + ln x)^2)
3)Let x = theta
y = x sin (ln x)
dy/dx = d/dx [x] * sin (ln x) + x * d/dx [sin (ln x) ] Product rule
dy/dx = sin (ln x) + x * [cos (ln x) d/dx (ln x) ] Chain rule
dy/dx = sin (ln x) + x * [ cos (ln x) * (1/x) ]
dy/dx = sin (ln x) + cos (ln x)
- 9 years ago
I can solve it here, but it will be messy. Try wolframalpha. It shows u how to do it step by step too. wolfram is ur best friend in math. but if u rely on it too much u will fail :P
