What is the area please help me
1 answer:
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The answer is .
Apply logarithmic differentiation on each side.
<u>LHS</u>
- u = x^y
- log u = y log x
- 1/u du/dx = y/x + log x (dy/dx)
- du/dx = x^y (y/x + log x dy/dx)
- du/dx = yx^(y - 1) + x^y logx dy/dx
<u>RHS</u>
- v = y^x
- log v = x log y
- 1/v dv/dx = x/y dy/dx + logy
- dv/dx = y^x (x/y dy/dx + logy)
- dv/dx = xy^(x - 1) dy/dx + y^x logy
<u>Equating both sides</u>
- yx^(y - 1) + x^y logx dy/dx = xy^(x - 1) dy/dx + y^x logy
- dy/dx (x^y logx - xy^(x - 1)) = y^x logy - yx^(y - 1)
Answer:
Needed 7 weeks
Step-by-step explanation:
Let x be the number of weeks.
<u>Nick</u>
- weighs 160 pounds;
- is gaining about 3 pounds per week;
- gains 3x pounds in x weeks;
- weighs 160 + 3x pounds after x weeks.
<u>Adam</u>
- weighs 195 pounds;
- is losing about 2 pounds per week;
- loses 2x pounds in x weeks;
- weighs 195 - 2x pounds in x weeks.
The equation that can be used to find the number of weeks that it will take them to weigh the same amount is
Solve this equation: