Calculus Test 2

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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


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