Exam 2 Study Guide
TANGENT LINES EXPONENTI
Growth ower Rule Non-Power Rule Logarithmic Differentiation We also discuss several other topics like How do proteins denature when exposed to salt, ph, and heat?
1) Find duivative ( may have to
Don't forget about the age old question of Who is the first president of the philippines?
use implicit/ rt I in (b)(b*) I 1) Take in of both sides.
2) Plugin x value to get slope. I
variabl 27 Add subtract logs. 3) Exponents become coefficients. 3) Plug in coordinate to pt.kslope
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e 4) Take derivatives.
formua for equation of line. 5) solve for y
to find rate, plugin a ) Plug equation back in for y.
known coordinate a
- solve. Ensure that the point ) MPLICIT DIFFERENTIATION_
EN nor s is even on the curve
LOGARITHNIC FUNCTIONS Differentiate both sides. (Assume y=f(x).
by plugging it into the C original equation, I
In(ea) =a loga(x) + loga(y) = loc :) Plug in a courdinate to find slope of tangent line.
e incas a log(x) - logoly = m -
. Exam 2 Study Guide
1) Find derivative
unate to ph.Islom
to find rate, plugin a known coordinute and
Ensure that the point is even on the Curve Don't forget about the age old question of What are the stages of sensorimotor development?
may have to
Power Rule Non-Power Rule Logarithmic Differentiation 1) Take in of both sides.
Dorte Per varia
2) Plugin a value to get slope. I
2 Add/subtract logs. 7) Exponents become coefficients. 3) Plug in coordinate to pt. slope amount rate 4) Take derivatives.
formula for equation of line.
5) Solve for y
) Plug equation back in for y. INPLICIT DIFFERENTIATION
by plugging it into the 1) Differentiate both sides. (Assume y=f(x)). ( original equation,
y=a* loga y=x
2) Isolate y
In(e) = loga(x) + 10ga(y)= loga (xy)
3) Plug in a coordinate to find slope of tangent line.
e da loga (x) - loga(y) = loga (7)
4) Plug valves into point - slope formula. Horizontal Tangent Line: find where y'=0.
* Alur finding roots to an equation, find what
if found anx-value y o
d. where y'- of undefined, ones truly work - Cannot have log of neg.#* - - - - - -- ---> check it there is evena ?
Buplugging into diging
INVERSE FUNCTIONS *iff@) ab then f (b) =a. A fonction is invertible if it is one-to-one (passes horizontal line test).
If a function (ie, sinx) is not one-to-one, restrict its domain so it is able to be in vertible.
Y value for that a-valve
APPLICATIONS of DERIVATIVES
Maximum Height Time of impact impact Velocity!
Solve s'(t) = 0
+ upwards for words / - down/backwards
15+ Derivative - Velocity
• Use t from time of impact
Test points on either
to put in s' (t) equation.
Znd Detivatiye acceleration
side of 0. * Speeding up signs on velocity and acceleration are the same . Find wheet on left * Speed should be given in positive
Slowing Down signs on velocity + acceleration are opposite and - on right. units WC velocity only indicats direction LINEARI ZATION
If y=f(x) and fis differential, then
dx is independent variable and dy
$(x) f(a) + f'(o)(x-a) to f(x) at xsa is... when x is near a.
described as dy = f'(x) dx.
f'(x) = RELATIVE ERROR (think of error as your known iekte) RELATED RATES dx error valve calculated
o Draw label diagram. * what it should be regularly (pvt * in original - NOT derivative) Identify known and unknown rates. # often convert to a puunt*
wite an equation selating known/unknon n. © Tako duivative.
Substituke numbers into duivative.