Derivatives
Implicit Differentiation
Antiderivatives
Limits
Formulas/Theorems
100
f (x) = 4x^3 − 3x^2 + 2x − π
f ' (x) = 12x^2 - 6x + 2
100
Find dy/dx of x^2 - 5xy + 3y^2 = 7
(2x-5y)/(5x-6y)
100
Find the antiderivative of 3cosx - (7sinx)
3sinx + 7cosx + C
100
lim x-> 1 of (x^2 - 7x + 10)/(x^2 - 4)
4/-3
100
f '(x)=lim h->0 [f(x+h) - f(x)] / h
What is the Definition of a Derivative?
200
f (x) = (x^2)/3 - 3/(x^2)
f ' (x) = (2/3)x + (6/x^3)
200
Find dy/dx of sin(x/y) = 1/2
y/x
200
Find the antiderivative of 1/cos^2(x)
tanx
200
lim x->-5 of (x^2 +2x - 35)/(x^2 - 10x + 25)
-1/5
200
1/x times derivative of x
What is the Derivative of the Natural Log?
300
f (x) = √x - 1/√x
f ' (x) = 1/(2√x) + 1/(2x√x)
300
Find dy/dx of 4x^2 - 9y^2 = 17
(4x)/(9y)
300
Find the antiderivative of 1/√(4-x)
-2√ (4-x) + C
300
lim x->9 of (9 - x)/(√x - 3)
-6
300
If the limit of a function is indeterminate then you can take the derivatives of the top and bottom functions separately in order to get the actual limit
What is the L'Hospital's Rule?
400
f (x) = (e^x)/x
f ' (x) = (e^x)/x - (e^x)/(x^2)
400
Find dy/dx of ytan(x+y) = 4
y/x
400
Find the antiderivative of xe^(-x^2)
(-1/2)e^(-x^2)
400
lim x->4 of (x - 4)^3 / l4 - xl
0
400
If f is differentiable for all values of x in (a, b) and f is continuous at x=a and x=b, then there's at least one number x=c in (a, b) such that f'(c) = [f(b) - f(a)] / b-a
What is the Mean Value Theorem?
500
f (x) = e^(lnx^2) - 3(x^-7)
f ' (x) = (2e^lnx^2)/x + 21/(x^8)
500
Find the solution when dy/dx = cos(x) / y^2 , where y(π/2) = 0
y = (3 sin(x) - 3)^(1/3)
500
Find the antiderivative of (x^2)(e^5x)
[(x^2) - (2x/5) + (2/25)]*[(e^5x)/5]
500
lim x-> 0 of (x + 4x^2 + sinx)/(3x)
2/3
500
If f is differentiable for all values of x in (a, b) and f is continuous at x=a and x=b, and f(a) = f(b) = 0, then there's at least one number x=c in (a, b) such that f'(c) = 0
What is the Rolle's Theorem?
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