Unit 5 Facts Assessment 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(sin x)
cos x
d/dx(cos x)
-sin x
d/dx(a^x)
a^x ln a
d/dx(log>a x)
1/xlna
d/dx(sec x)
secxtanx
d/dx(cscx)
-cscxcotx
d/dx(tanx)
sec^2x
d/dx(cotx)
-csc^2x
d/dx(sin^-1x)
1/√1-x^2
d/dx(cos^-1x)
1/√1-x^2
d/dx(tan^-1x)
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) - f(x)g’(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
how do we write the equation for a tangent line given dy/dx and a point?
y=m(x-x1) + y1
when taking derivative of a y variable, what is included with the derivative?
we multiply the derivative of y by dy/dx
how do we get the slopes to create a slope field?
substitute ordered pairs into the dy/dx formula to calculate the slope
to solve a differential equation, what is the first step an AB calculus 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
how do we know is a tangent line approximation is an underestimate or an overestimate?
if the 2nd derivative is positive, the tangent line is an underestimate. if the 2nd derivative is negative, the tangent line is an overestimate.
how do we find the constant of integration when solving a seperable differential equation?
substitute the given ordered pair into x and y, and solve the equation for the +C value
