The chain rule says that if we have u(x) and f(u(x)), df/dx = df/du * du/dx f is the outside function, u is the inside. So, in the first case f(u) = √u u(x) = 2x+9 #2. f(u) = cos(u) u(x) = cos(x) #3. Is almost a trick question. f(u) = tan(u) u(x) = x
come on, man. distance to top of fence: d/3 = csc(1.25) You have the formula for L(x), the length of the ladder, so subtract d from that.
If the foot of the ladder is d feet from the fence, 3/d = tan x d = 3cot x L(x) = (d+3) sec x = 3(1+cotx)secx dL/dx = 3secx(tanx - csc^2(x)+1) So, either secx=0 (no solution), or tanx - csc^2(x)+1 = 0 x = π/4 So, L(π/4) = 3(2)(√2) = 6√2 As expected, a squ...
A line from (5,2) perpendicular to the curve will have the shortest distance to the curve. The slope of the graph is -4/3, so the normal has slope 3/4 So, now you have a point and a slope, so the perpendicular line through (5,2) is y-2 = 3/4 (x-5) y = 3/4 x - 7/4 These two lin...
the conditions mean that the slope is 8. y' is the slope, and since 6y' = 3x^2 y' = 1/2 x^2 If 1/2 x^2 = 8, then x = 4 So, at (4,11) the slope is 8
False - only length
Math Algebra II
what do you mean by "solve"? The function is defined as shown.
since the roots are -2/3 ±√23/3 i 1+α = 1/3 + √23/3 i 1+β = 1/3 - √23/3 i (1+α)(1+β) = 1/9 + 23/9 = 24/9 = 8/3
The two trains together cover 50 miles every hour. So, starting 50 miles apart, ...
f(x) = x+4sin x f'(x) = 1 + 4cos x So, where is cos x = -1/4?
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