If u(x) is a differentiable function, n is any real number, and f(x) = [u(x)]", then. ○ ƒ'(x) = [u(x)]"−¹u' (x) ○ f'(x) = (n − 1)[u(x)]*u'(x) O f'(x) = n[u' (x)] n-¹ u(x) ○ f'(x) = n[u(x)]*¯¹ u'(x) ○ f'(x) = n[u(x)]"-1

Q: For the function f(x) = 4x- 3x +2x +6x +2, find f"(x), the third derivative of f, and f''"(x) = %3D

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Q: Sketch the graph of a function that satisfies all of the given conditions. (a) f'(x) > 0 and f"(x) <…

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Q: If the derivative of the function f (x) is f'(x) = 18z2 + 2x + cos(z) + 6, then which if any of the…

A: Solve the first order differential equation by separation of variable and integration.

Q: (-7)=|

A: Topic:- derivatives

Q: Let f(x) = – 5 In(7x) f'(x) =

A: Given,           fx=-5ln7x

Q: X x+18

A: f(x)=xx+18

Q: Suppose f and g are functions that are differentiable at x=5 and that f(5)=8 ,f'(5)=-3 ,g(5)=-1 ,…

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Q: Suppose that Find f'(x). f'(x) = = f(x+h)-f(x) = 6hx - 4h +8h².

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Q: and g(x) are differentiable functions, suppose that f(-2) = 1; f(1) = 5; f'(-2) = 3; f'(1) = 3;…

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Q: Let f(x) = (2x² + 8x – 1)*. Find f'(x). f'(x) =

A: Given function is Differentiating with respect to x using chain rule of differentiation, we get

Q: Let F(x) = f(r°) and G(r) = (f(x))° . You also know that a = 12, f(a) = 2, ƒ'(a) = 15, f'(aº) = 5…

A: We know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x   Given: Fx=fx9 ;…

Q: If find f'(x). ƒ'(x) = | Find f'(4). ƒ'(4) = f(x) = = 7-x² 8+x²

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Q: Find f'(x) and simplify. f(x)= Which of the following shows the correct application of the quotient…

A: We can solve as follows Do not confuse in round bracket and close bracket. They are same in this…

Q: Let f(x) = sin(x5). f'(x) = f'(2) = 0

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Let f(x) = 5x² cos(2x). f'(x) = -10x²(2x) + 10x cos(2x) f'(5) = 0 f"(x) = -10x² sin (2x) + 10x…

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Q: Suppose f''(x) = 42x + 16e-4x, ƒ'(0) - 14, and f(0) = - 9. Then f(x) =

A: See this solution in below.

Q: Let F(x) = f(a") and G(2) = (f(x))". 3, f(a) = 3, f'(a) 15 You also know that a 10, f'(a") Then…

A: F(x)=fx6 and G(x)=fx6

Q: Find f'(x*) if f(æ²)] = xª. f'(교2) =

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Q: Suppose that Find f'(2). f'(2) = f(x) = = e³x x² + 4

A: Given f(x)=e3xx2+4   We are required to findf'(2)         The following formulas of derivatives has…