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# If you generate d with x?

Updated: 10/25/2022

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Q: If you generate d with x?
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### What solid geometric figures contain circles?

Sections of:cones, spheres, ellipsoids, tori, paraboloids, hyperboloids.In fact, consider the graph of any function in 2-dimensions that is always non-negative. Rotate the curve around the x-axis to generate a 3-d shape. A straight line will generate a cone, a square root function will generate a paraboloid, a semicircle will generate a sphere and so on. A wobbly line will generate a lumpy 3-d shape [NB: wobbly and lumpy are very technical terms ;) ]A plane at right angles to the x-axis will intersect all these curves in a circle.

### What is the factor of 30 d to the 5 power?

2 x 3 x 5 x d x d x d x d x d = 30d5

### What is the factor of the monomial 30d5?

2 x 3 x 5 x d x d x d x d x d = 30d5

4d x d x d = 4d3

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### How do you prove that the derivative of sec x is equal to sec x tan x?

Show that sec'x = d/dx (sec x) = sec x tan x. First, take note that sec x = 1/cos x; d sin x = cos x dx; d cos x = -sin x dx; and d log u = du/u. From the last, we have du = u d log u. Then, letting u = sec x, we have, d sec x = sec x d log sec x; and d log sec x = d log ( 1 / cos x ) = -d log cos x = d ( -cos x ) / cos x = sin x dx / cos x = tan x dx. Thence, d sec x = sec x tan x dx, and sec' x = sec x tan x, which is what we set out to show.

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d=3c

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### What is the derivative of f plus g of 3 and f times g of 3 given that f of 3 equals 5 d dx f of 3 equals 1.1 g of 3 equals -4 d dx g of 3 equals 7 Also please explain QUICK THANK YOU?

d/dx [f(x) + g(x)] = d/dx [f(x)] + d/dx [g(x)] or f'(x) + g'(x) when x = 3, d/dx [f(x) + g(x)] = f'(3) + g'(3) = 1.1 + 7 = 8.1 d/dx [f(x)*g(x)] = f(x)*d/dx[g(x)] + d/dx[f(x)]*g(x) when x = 3, d/dx [f(x)*g(x)] = f(3)*g'(3) + f'(3)*g(3) = 5*7 + 1.1*(-4) = 35 - 4.4 = 31.1