Calculus Test 2
Use the definition of the derivative to find the derivative of: f(x)=10x−12.f′' (x)=
10
14th derivative of f(x) = xe^x if x = 2.48
196.79 was on quiz
s = t^6 − 3t^5. Find the value of t (other than 0 ) at which the acceleration is equal to zero.
2
f(x)=xsin(x). Find f′′(4.1)
2.205
differentiate f(x)=5e^xsinx
5e^xsinx + 5e^xcosx
point slope form
y - y1 = m(x - x1)
Calculate g(b) and g′(b) where g(x) is the inverse of f(x)=(x^2+6x)^1/2 in the domain x≥0, where b=4.
'
Find the rate of change of force with respect to distance at the surface of the earth, assuming the radius of the earth is 6.77e6 m
-1.927E-4
Let f(x)=1/x. Compute the difference quotient for f(x) at x=3 with h=0.3
-1/9.9
d/dt((t2+1)(t+9)) if t=−3=
-26
der of 1/sinx
-cotx * cscx
f'(x) of cosx
-sinx
y=sin(7x)+cos(8x) at the point (π/6,y(π/6))
0.868x−1.4546
f(x)=2sin^2(x) then f′(x)=
4cosxsinx
fx = 7 log(base 5) (x)
7 * (1/x) * (1/ln5)
height (in meters) after t seconds is given by y=24t−4.9t^2. Find the velocity in meters per second of the rock when t=1.5. (Include units.)
9.3 m/s
derivative
= slope of tangent line = IROC
is the graph of the function is the graph of the function's first derivative is the graph of the function's second derivative
B, C, A
f(x)=xlnx−x. means xln(x) - x
der is lnx
implicit differentiation: find d/dx of y^4 + xy = x^3 - x + 2
emphasized
Derivative tells you how much fx changes in one unit
ex: cost to produce one more unit
f(x)=−7e^(xsinx)
ez
fx = ln(2x)
f'x = 2/2x (chain rule)
1/x + 1/y = 5 and y(5)=5/24, find y′(5) by implicit differentiation.
−0.001736
Differentiable
- can find derivative - cant find derivative w/o being continuous - can be continuous w/o having derivative : fractional power/vertical slope and abs
how to solve for multiple terms in less time (can leave answer as is)
he emphasized this Normal x (derivative / regular) Top terms+ Bottom terms -
differentiate y = x^(cosx)
he emphasized this example
sin(A+B)
sinAcosB + cosAsinB
ind the equation for the line tangent to the graph of the equation 2xy−2x+0=0 x = -2
y = 1
Find the equation of the line tangent to the graph of y=3ln(x) at x=2.
y = 1.5x − 0.9206
equation of the tangent line to the curve y = 2sec(x) − 4cos(x) at the point (π/3,2)
y = 10.39x - 8.88
f(x) = 5x* sqrt(1-4x) Find the equation of line tangent to the graph of f at x = −2.
y = 21.667x + 13.33
derivative of 4cosx
-4sinx dont have to do product thing
given f(x) = 3x-5 find f'(x)
3 because slope
Equation of tangent line to y=10tan(x) at x=pi
May/ may not be right
Derivative of b^x
b^x ln(b)
derivative graph usually
becomes simpler each time
f(x) = 14x+9 find f'(x)
Limit is 14 bc slope
Since January 1, 1960, the population of Slim Chance has been described by the formula P=39000(0.97)^t, where P is the population of the city t years after the start of 1960. At what rate was the population changing on January 1, 1989? ask
-491.09
derivative of cos
-sin
derivative of cosx
-sinx
If f(x)=5log8(x), find f′(1).
2.40449
find inverse of function on graph wen x = 1.8
basically just swap x and y and find x when y = 1.8
V=−Blv is induced in the wire. Assume that B=12 and l=0.6.
can plug in B and l values and simplify before finding derivative
constant value is immediately plugged in, variable is plugged in after f'(x) is derived
contestants go to 0, variables go to 1
derivative of sin
cos
derivative of sinx
cos
f'(x) of sinx
cosx
Derivative of e^x
e^x
y=e^(-9x)cos(−2x)
ez
y = sqrt (6+4tanx) der
ezz
Difference Quotient
f(x + h) - f(x) / h
fx = lnx
f(x) = 1/x * x'
Let f(t) be the number of centimeters of rainfall that has fallen since midnight, where t is the time in hours. Match the following statements to their interpretations, given below. at 8 AM, the rain is falling at a rate of 0.2 cm/hr
f′ ' (8)=0.2
Find the equation of the tangent line to the curve (a hyperbola) x^(2/3)+y^(2/3)=17 at the point (64,1). The equation of this tangent line can be written in the form y=mx+b
hell y = -0.25x + 17
y = xln(x) - 1
lnx
