(4) This exercise is intended to be an initial exposure for taking derivatives with a different variable other than r. The same rules apply, just use the given variable instead of r. (y? + 8)* (a) If f(y) = find f'(y). (b) If z = 9t?e-4", find (c) If k(8) = In (64 + 0), find [k(8)].

Q: If f(x) find: 7+x2 f'(x)-

A: Given f(x)=2-x27+x2

Q: Find the derivative of  g(z) = 4z7-3z-7+9x

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Q: For the function f (x) = 5a- 7x +4r + 3 %3D a. Find f '(x) b. Find f" (x) c. Find f" (0) and f “ (2)…

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Q: a. f(x) = 4x + 11 find: f'(-2) b. f(x) = 2x2-5x 3 find: f'(2)

A: Given: f(x)=4x+11 f(x)=2x2-5x-3

Q: (2а + 5)10 (г — 3)° (4аг + 7)50 6. f(x)

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A: I have explained everything with in the solution. Please go through that.

Q: 4. Find the derivative. x? + 6x – 5 (a) 5х -1 (b) ƒ(x) = (3xr² – 5x - 7)' Us e chain rule (c) y =(x-…

A: Topic:- derivatives

Q: point) If ƒ(5) = -3, g(5) = -4, f'(5) = -2, and g'(5) = -2, find the values of the following: %3D (f…

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Q: f(x) = (8x + 10)*, then find the second derivative, f" (x) =

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Q: If f(x) = 7+ 3 – 3x², find f'( – 5). -

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Q: Find the second derivative or f"(x) for f(x) = / 2x + 5. %3D 1 (2x + 5)3/2 (2x + 5)!/2 (2x + 5)3/2…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.