Derivatives
The derivative of the following function
f(x) = (3x+x4)/(2x2+1)
What is...
f'(x) = (4x5+4x3-6x2+3)/(2x2+1)2
The inverse and derivative of the inverse of the following function
h(x) = (1+9x)/(4-x)
What is...
Inverse: h-1(x) = (4x-1)/(9+x)
Derivative of Inverse: 37/(x+9)2
The derivative y' of the following function using implicit differentiation
2y3+4x2-y=x6
What is...
y' = 6x5-8x/6y2-1
Using the definition of a limit as proof, the limit as x goes to 3 at x is equal to 3
Properly shown steps according to the definition of a limit
The absolute exrema of the following function
h(z)=4z3−3z2+9z+12 on [−2,1]
What is...
Absolute Maximum: 22 at z=1
Absolute Minimum: −50 at z=−2
The derivative of the following function
c(x) = 12sin(x) * cos(x)
What is...
c'(x) = -12(sin2(x)-cos2(x))
The inverse and derivative of the inverse of the following function
f(x)=7√(5x+8)
What is...
Inverse: f-1(x)=1/5(x7−8)
Derivative: 7x6/5
The derivative y' of the following function using implicit differentiation
7y2+ sin(3x) = 12-y4
What is...
y' = -3cos(3x)/14y+4y3
The limit as t goes to -1 of (t+1)/|t+1|, it it exists
What is...
The overall limit does not exist (DNE)
The absolute extrema of the following function
h(w)=2w3(w+2)5 on [-5/2, 1/2]
What is...
Absolute Maximum: 24.4141 at w=1/2
Absolute Minimum: −2.5749 at w=−3/4
The derivative of the following function
h(x) = ex(tan(x))
What is...
h'(x) = ex(tan(x)+sec2(x))
The inverse and derivative of the inverse of the following function
g(x)=4(x−3)5+21
What is...
Inverse: g-1(x) = 3+5√(1/4(x−21))
Derivative: 1/(5*(5√4)(x-21)4/5
The derivative y' of the following function using implicit differentiation
ex-sin(y)=x
What is...
y' = (ex-1)sec(y)
The limit as x goes to 2 for (8-3x+12x2), if it exists
What is...
50
We want to build a box whose base length is 6 times the base width and the box will enclose 20 in3. The cost of the material of the sides is $3/in2 and the cost of the top and bottom is $15/in2. The dimensions of the box that will minimize the cost are....
What is....
w=0.7299
l=4.3794
h=6.2568
The derivative of the following function
g(x) = ln(54x3+12x2+9x+24)
What is...
g'(x) = (164x2+24x+9)/(54x3+12x2+9x+24)
The inverse and derivative of the inverse of the following function
f(x) = (6-10x)/(8x+7)
What is...
Inverse: f-1(x) = (6-7x)/(8x+10)
Derivative: -59/(2(4x+5))2
The derivative y' of the following function using implicit differentiation
4x2y7−2x = x5+4y3
What is...
y' = (8xy7−5x4−2)/12y2−28x2y6
The limit as h goes to 0 for ((6+h)2-36)/h, if it exists
What is...
12
We have a piece of cardboard that is 50 cm by 20 cm and we are going to cut out the corners and fold up the sides to form a box. The height of the box that will give a maximum volume is...
What is...
h=4.4018
The derivative of the following function
K(x) = 1+e-2x/x+tan(12x)
What is...
K'(x) = -2e-2x(x+tan(12x))-(1+e-2x)(1+12sec2(12x))/(x+tan(12x))2
The inverse and derivative of the inverse of the following function
f(x) = x3+6
What is...
Inverse: h-1(x) = 3√(x−6)
Derivative: 1/(3(x-6))2/3
The derivative y' of the following function using implicit differentiation
tan(x2y4)=3x+y2
What is...
y' = 3−2xy4sec2(x2y4)/4x2y3sec2(x2y4)−2y
Using the definition of a limit as proof, the limit as x goes to 0 from the left for 1/x equals negative infinity
The definition of a limit as proof
We have 45 m2 of material to build a box with a square base and no top. The dimensions of the box that will maximize the enclosed volume are...
What is...
l=w=3.8730
h=1.9365