Chain Rule
What is Chain Rule
The derivative of the outside function with the same inside function, multiplied by the derivative of the inside function
if the limit as x-->1+ does not equal the limit as x-->1-, does the limit as x-->1 exist?
No, it does not.
What is the indefinite integral of 1/u
ln|u|+c
What is the derivative of 6x^3
18x^2
what does Intermeiate value theorem gurantee
This guarantees that if a function iscontinuous on [a,b], there must exist a c such that f(c) is in between f(a) and f(b)
Find the derivative of f(g(x))
f’(g(x)) · g’(x)
What must be true for a function to be continuous at a point.
lim as x--> a- = lim as x-->a+ = f(a)
What is the integral of sec(x)
ln|sec(x)+tan(x)|+c
what is the derivative of sin(x)+tan(x)
cos(x) + sec(x)^2
Can the mean value theorem be used with f(x)=|x| on the interval [-1,1]?
No it cannot, f is not differentiable at x=0
find the antiderivative of 4sec(3x)tan(3x)
4/3(sec(3x)) + c
what does removable discontinuity mean
the lim as x-->a exists and does not equal f(a)
what is the integral of 3x^2 from x=1 to x=4
63
what is the derivative of x^2 · ln(x)
2x · ln(x) + x
what is the derivative of 2t^2 +5t +7 from t=5 to t=x
2x^2 +5x +7
Find the derivative of (5x^2+20x+40)^1/2
(5x+10)/((5x^2+20x+40)^1/2)
what is the limit as x--->1 of (x^2 - 1)/(x-1)
2
find the definite integral of 5/x + 9 from 2 to 5
5 ln (5/2) + 27
what is the derivative of ln(x^2 +1)
2x/(x^2 + 1)
F(x) = the integral from 2 to x^2 of cost(t^2). What is F'(t)
2xcost(x^4)
find the derivative of: e^(sin(3x^2))
e^(sin(3x^2))·cos(3x^2)·6x
lim as x--> 0 of (e^x -1)/x
Use L'Hopitals rule, 1
What is the integral of 1/(4+x^2)
1/2 · arctan(x/2) +c
what is the derivative of sin(x)/4x
(x·cos(x) - sin(x))/4x^2
F(x) = x^3 - 2x - 1 is continuous on the interval [1,2]. Is there a c in (1,2) such that f(c) =0
Because f is continous on [1,2] and f(1)=-2 and f(2) = 3, IVT gurantees that there exists a c on (1,2) such that f(c) =0