Implicit Differentiation
Find dy/dx from the following equation:
2x^2-y^2=9
dy/dx=(2x)/y
Find dy/dx from the following equation:
y=x^2e^x
dy/dx=2xe^x+x^2e^x
Find the Critical Points from the following equations, and describe if they're Maxima or Minima:
y=4x^3-3x
Maxima: x1=-1/2
Minima: x2=1/2
Find the Inflexion Points from the following equations:
y=x^2-6x
No Inflexion Points!!
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Javier & David!!
Find dy/dx from the following equation:
x^2y=x-7y
dy/dx=(1-2xy)/(x^2+7)
Find dy/dx from the following equation:
y=x^2ln(9x)
dy/dx=2xln(9x)+x
Find the Critical Points from the following equations, and describe if they're Maxima or Minima:
y=4sqrt(x)-x^2
Maxima: x1=1
*Minima: x2=0
Find the Inflexion Points from the following equations:
x^4-6x^3
p1=(0, 0)
p2=(3, -81)
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Find dy/dx from the following equation:
(xy)^2+3x=2y^2
dy/dx=(-3-2xy^2)/(2x^2y-4y)
Find dy/dx from the following equation:
y=lnsqrt(5x-7)
dy/dx=5/(10x-14)
Find the Critical Points from the following equations, and describe if they're Maxima or Minima:
y=sqrt(4-x^2)
Maxima: x=0
*Minima: x2=-2, x3=2
Find the Intervals where the Function is Concave Up or Concave Down:
y=x^3-6x^2
Concave Down: (-oo, 2)
Concave Up: (2, oo)
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Find dy/dx from the following equation:
xy-cos(x^2y)=1
dy/dx=(y+2xysin(x^2y))/(-x-x^2sin(x^2y))
Find dy/dx from the following equation:
y=x^sqrt(x)
dy/dx=((xln(x)+2x)/(2sqrt(x)))x^sqrt(x)
Find the Critical Points from the following equations, and describe if they're Maxima or Minima:
y=ln(x-2)
No Maxima or Minima points.
Find the Intervals where the Function is Concave Up or Concave Down:
y=x+x^2-x^3
Concave Up: (-oo, 1/3)
Concave Down: (1/3, oo)
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SPIDER-MAN: BRAND NEW DAY!!!!
Find dy/dx from the following equation:
xy^2+sin(piy)-2x^2=10
dy/dx=(4x-y^2)/(2xy+picos(piy))
Find dy/dx from the following equation:
y=e^(x^3ln(x))
dy/dx=(3x^2ln(x)+x^2)e^(x^3)ln(x)
Find the Critical Points from the following equations, and describe if they're Maxima or Minima:
y=x^(3/2)-3x^(5/2)
Maxima: x1=1/5
*Minima: x2=0
Find the Intervals where the Function is Concave Up or Concave Down:
y=x^3+x^4
Concave Up: (-oo, -1/2) U (0, oo)
Concave Down: (-1/2, 0)
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