Facts Assessment Unit 2 Flashcards
d/dx (x^n)
nx^(n-1)
d/dx(constant)
0
d/dx(lnx)
1/x
d/dx(e^x)
e^x
d/dx(sinx)
cosx
d/dx(cosx)
-sinx
d/dx(a^x)
a^x * lna
d/dx(log_a x)
1/(x * lna)
d/dx(secx)
secx * tanx
d/dx(cscx)
-cscx * cotx
d/dx(tanx)
sec^2 x
d/dx(cotx)
-csc^2 x
d/dx(sin^-1 x)
1/(1-x^2)^1/2
d/dx(cos^-1 x)
-1/(1-x^2)^1/2
d/dx(tan^-1 x)
1/(1+x^2)
d/dx(f(x)g(x))
f(x)g’(x) + f’(x)g(x)
d/dx(f(x)/g(x))
(g(x)f’(x)-g’(x)f(x))/(g(x))^2
d/dx(f(g(x)))
f’(g(x)) * g’(x)
What is the slope of a tangent line?
The derivative at the tangent point
Write the point slope form of a line
y=m(x-x1)+y1
What is Euler’s method
An approximation method that uses multiple tangent lines to approximate differential equations
Write the formula for a Taylor polynomial with the center at x=a up to degree 3
Tn(x) = f(a) + f’(a)(x-a) + f’‘(a)/2! * (x-a)^2 + f’’‘(a)/3! * (x-a)^3
What term do we use to calculate the error bound of a Taylor polynomial
The next Taylor term that would have been used in the approximation
What is a Taylor polynomial centered at x=0 sometimes called?
A Maclaurin polynomial
How do you get the slopes to create a slope field?
Substitute ordered pairs into the dy/dx formula to calculate the slopes
To solve a differential equation, what is the first step an AB or BC student must take?
Separate the variables by getting all x terms on the same side as dx and all y terms on the same side as dy
When does a logistic curve reach its inflection point?
At half the carrying capacity
