Textbook Question
27–40. Implicit differentiation Use implicit differentiation to find dy/dx.
√x⁴+y² = 5x+2y³
4. Applications of Derivatives
Implicit Differentiation
Back4. Applications of Derivatives
Implicit Differentiation
- Textbook Question
Surface area of a cone The lateral surface area of a cone of radius r and height h (the surface area excluding the base) is A = πr√r²+h².
b. Evaluate this derivative when r=30 and h=40.
- Textbook Question
Surface area of a cone The lateral surface area of a cone of radius r and height h (the surface area excluding the base) is A = πr√r²+h².
a. Find dr/dh for a cone with a lateral surface area of A=1500π.
- Textbook Question
Volume of a torus The volume of a torus (doughnut or bagel) with an inner radius of a and an outer radius of b is V=π²(b+a)(b−a)²/4.
a. Find db/da for a torus with a volume of 64π².
- Textbook Question
Volume of a torus The volume of a torus (doughnut or bagel) with an inner radius of a and an outer radius of b is V=π²(b+a)(b−a)²/4.
b. Evaluate this derivative when a=6 and b=10.
- Textbook Question
45–50. Tangent lines Carry out the following steps. <IMAGE>
a. Verify that the given point lies on the curve.
x³+y³=2xy; (1, 1)
- Textbook Question
45–50. Tangent lines Carry out the following steps. <IMAGE>
b. Determine an equation of the line tangent to the curve at the given point.
x³+y³=2xy; (1, 1)
- Textbook Question
45–50. Tangent lines Carry out the following steps. <IMAGE>
a. Verify that the given point lies on the curve.
x⁴-x²y+y⁴=1; (−1, 1)
- Textbook Question
45–50. Tangent lines Carry out the following steps. <IMAGE>
b. Determine an equation of the line tangent to the curve at the given point.
x⁴-x²y+y⁴=1; (−1, 1)
- Textbook Question
45–50. Tangent lines Carry out the following steps. <IMAGE>
a. Verify that the given point lies on the curve.
(x²+y²)²=25/4 xy²; (1, 2)
- Textbook Question
45–50. Tangent lines Carry out the following steps. <IMAGE>
b. Determine an equation of the line tangent to the curve at the given point.
(x²+y²)²=25/4 xy²; (1, 2)
- Textbook Question
51–56. Second derivatives Find d²y/dx².
2x²+y² = 4
- Textbook Question
51–56. Second derivatives Find d²y/dx².
x⁴+y⁴ = 64
- Textbook Question
51–56. Second derivatives Find d²y/dx².
sin x + x²y =10
- Textbook Question
13-26 Implicit differentiation Carry out the following steps.
b. Find the slope of the curve at the given point.
(x+y)^2/3=y; (4, 4)