With f(x) = 2x, f'(x) = 2, g(x) = 3x² - 1, and g'(x) = 6x, we are now ready to substitute these terms into the product rule to find dy for y = 2x(3x² - 1). Once the substitutions are made, dx continue to simplify. [f(x)g(x)] = f'(x)g(x) + f(x)g'(x) [2x(3x² − 1)] = 2(3x² − 1) + 2x(

Q: f (x) = (4x + 5)* (x²? – 2x + 5)* Find the Derivative

A:

Q: f(x) = 5x³ + 6x - + Use g '(x) = g'(−2)= 6x-2 has an inverse g(x). 1 ƒ'(g(x)) to find g '(-2).

A:

Q: If f(x) = 9xh (2), find f'(9).

A:

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A: Consider the given function.

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A:

Q: Find g(x) if g'(x) = (60x² 80x) g(x) = 4x 4 - 8x and g(0) = 3.

A: Giveng'(x)=(60x2-80x).44x3-8x2  and g(0)=3

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A: The sum rule of the differentiation states that, ddxf+g=ddxf+ddxg the power rule of the…

Q: Find f(x). -9x + 6x - 5x +1 f(x) f'(x)

A:

Q: If ƒ(x) = (3x² − 8) (4x + 6), find: - ƒ'(x) = ƒ'(2) =

A:

Q: flx)=x =X-5 (x)= Find .f)

A: Here, the given function is: f(x)=x-5, g(x)=x2

Q: If f(x) = 23x + 27, find f'(5).

A: First we have to find derivative of f(x) then we will find f'(5) as shown below

Q: If f(x) = 6 + 3x − 2x², find f'(4).

A: Given,

Q: If f(x) = 2x + ln x, find f-1(2).

A: The function is given as fx=2x+ln x......(1) The value of f(x)=2.......(2) Equate the equation (1)…

Q: Find y'

A: given

Q: For the function ​f(x)=2e^−x^3​, find f′′(x). Then find f′′​(0​) and f′′​(1​).

A: To find f''(x)

Q: If u(x) = x3, then du = 3x2.

A:

Q: If f(x) =x² +1 and g(x) = 2x + 3, find all values of x where the derivative of fAg(x)) is equal to…

A:

Q: Find h(x) if h'(x)= h(x): 5x (6-x²)² X and h(1) = -6.

A: NOTE: Refresh your page if you can't see any equations. . here we have take integration on both…

Q: If f(x)f(x) is the slope of a trail at a distance xx miles from the start of the trail, what does…

A: If f(x) is the slope of a trail at a distance x miles from the start of the trail, what does…

Q: If f(x) = 15x + 4, find ƒ'(5).

A: Given: The given function is fx=15x+4 To find: we have to find the value of f'5 Note: Multiple…