-Use implicit differentiation to find dy/dx where
x2y2 + x cos(y) = 6
-Use logarithmic differentiation to find the derivative of o(x)
= (cos(x))ln(x)
-Find the first and second derivatives of p(x) = 6
ln(x2+3x)
-A balloon is rising vertically at a constant speed of 5 ft/sec.
A boy is
cycling along a straight road at a speed of 15 ft/sec. When he
passes
under the balloon, it is 45 ft above him.How fast is the
distance between
the boy...
1.The graph of (x-1)^2+(y-1)^2=4 is shown on the right. Use
implicit differentiation to find the slopes of the tangent lines at
the points on the graph where x=2.2 . Check your answers by
visually estimating the slopes on the graph in the figure.
2.Use implicit differentiation to find y′. Then evaluate y′ at
(2,1)
x^4-16y^3=ln y
part 1)
Use implicit differentiation to find an equation of the tangent line to the curve
sin(x+y)=6x−6y at the point (π,π)
Tangent Line Equation: y=
part 2)
Find an equation of the tangent line to the curve x^(2/3)+y^(2/3)=13 at the point (−8,27)
y=
part 3)
Find an equation of the tangent line to the curve
(x^2/36)+(y^2/81)=1
at the point (−3,(−9/2)√3)
An equation of this tangent line to the ellipse at the given point is y=mx+b where
m= and b=...
Use implicit differentiation to find an equation of the tangent
line to the curve at the given point.
x2 + y2 = (5x2 + 2y2
− x)2
(0, 0.5)
(cardioid)
y =
The vector field given by E
(x,y,z) = (yz – 2x)
x + xz y + xy
z may represent an electrostatic field?
Why? If so, finding the potential F a from which E may be
obtained.
Compute the derivative of the given vector field F. Evaluate the line integral of
F(x,y,z) = (y+z+yz , x+z+xz , x+y+xy )over the path C consisting of line segments joining (1,1,1) to (1,1,2), (1, 1, 2) to (1, 3, 2), and (1, 3, 2) to (4, 3, 2) in 3 different ways, along the given path, along the line from (1,1,1) to (4,3,2), and finally by finding an anti-derivative, f, for F.