Calculus Answers

Find the derivative using chain rule-d/dx: 

5.y = (4x - 9) * (3x - 4) ^ 2

6.y = x/(x ^ 2 - 2) ^ 2)

7.) y =(x²-7)²(2x - 5)³

8. y = (x ^ 4 - 2x) ^ 2/(x - 1) ^ 3

9. y = sqrt(x - 2) ^ 2

10.) y = (x ^ 3 + x ^ 2) ^ 2 * (x - 1) ^ 3

Water is being poured at the rate of 2π cubic meter/min into an inverted conical tank that is 12-meter deep with a radius of 6 meters at the top. If the water level is rising at the rate of 1/6 m/min and there is a leak at the bottom of the tank, how fast is the water leaking when the water is 6-meter deep?

find the area of the surface generated when the given arc is revolved about the y axis ( y= 4 - x^2 from x=0 to x=2 )

Find the surface area of that part of the plane 4𝑥+5𝑦+𝑧=8

4x+5y+z=8 that lies inside the elliptic cylinder (x²/100) + (y²/81) =1

Given that y= acoskx + bsinkx, show that d²y/dx² + k²y =0

ACTIVITY IN BASIC CALCULUS

BASIC RULES IN DERIVATIVE

 Complete the blanks of the given function below with a number (except 0 and 1) to create your own problem and find the derivative of the function. Show your complete solution to each problem.

1. f(x) = -₄x⁵+ ______x^-4 - 2468

2. f (x) =____x^-3- _____x^1/4 - 12x

3.f(x)= ____ "\\sqrt[4]{x^3} - \\underset{x^6}{=} + \\frac{2}{3} x^6"

4.f (x) = "\\underset{x^-6}{=} -" ____ x² + "\\sqrt[4]{x}"

ACTIVITY IN BASIC CALCULUS

BASIC RULES IN DERIVATIVE

 Complete the blanks of the given function below with a number (except 0 and 1) to create your own problem and find the derivative of the function. Show your complete solution to each problem.

1. f(x) = -₄x⁵+ ______x^-4 - 2468

2. f (x) =____x^-3- _____x^1/4 - 12x

3.f(x)= ____ "\\sqrt[4]{x^3} - \\underset{x^-6}{=} + \\frac{2}{3}" x⁶

4.f (x) = "\\underset{x^-6}{=} -" ____ x² + "\\sqrt[4]{x}"

Given that the sum of the first four term of an AP is 32, while the sum of the three next terms is 52. Calculate the sum of the first 10 terms of the sequence.

Find the output needed to maximize profit given that the total cost and total revenue functions are TC=2Q and TR=100 ln (Q+1) respectively. 

Find the limit of the following functions using the tabular method.

1. lim    x2+x-6x+3/ x+3

𝑥→−3

1. lim x2-2x+3/ x+1   

𝑥→−1