(1) f(x)= x/2

Q: Is the function f(2) = -2(xy+x)+i(x² – 2y – y) differentiable? If it is, find it's derivative.

A: Consider the given function.

Q: Find f′(x) and f′(c). Function f(x) = (x − 4)/(x + 4) Value of c = 3

A: Now differentiating with respect to x, we get

Q: f(x) = (x + 3)(x – 1)².

A: Given function Find the critical values for the given function. To find critical values we need to…

Q: [f(a)]² =

A:

Q: Using Exact Differential Equations, solve: (x + 4x²³ siny)dx + x4 cosy dy =

A:

Q: f (0), where f (x) = 101+x

A: fx=101+xf0=?

Q: 3. Find f(x) and f (x) if f(x) = lnx + 2cos³ x. %3D

A: First use sum/difference rule of differentiation f±g=f'±g' then use the following formulae: dln…

Q: f (1), where f (x) = 21 + x2

A: Given function - f(x) = x2+21         ...........(1)f-11 = ?First we need to find the inverse…

Q: Find the directional derivative of f at the point (1,2) in the direction of the vector v = = (1, 3).

A:

Q: For f(x) = x? – 3x + 5, find f(2), f'(2), and f(3) – f(2). a. f(2) b. f'(2) = c. f(3) – f(2) =

A: Given that, f(x)=x2-3x+5

Q: Find f′(x), if f(x)=(x4+1)(3x−1).

A:

Q: Given f(x)=x+(1/x).   Find f(a).

A: Given, The function is f(x)=x+(1/x).

Q: 1. Use forward and backward difference approximations of O(h) and a centered difference…

A:

Q: If f(t) = (1 + 0.04)t, what is f(0)?

A: note that (any number)0 =1

Q: A volume is described as follows: 1. the base is the region bounded by y = 8-2² and y = 0 2. every…

A: The base is the region bounded by y=8−12x2 and y=0. Every cross section parallel to the x-axis is a…

Q: Find f such that f′(x)=8x​, ​ f(4​)=47.

A: Given, f′(x)=8x​,​ f(4​)=47.

Q: Consider the function g(x)=(f(x))^5. If f(4)=3 and f′(4)=−2, then find g′(4).

A: Given: g(x)=f(x)5f(4)=3f'(4)=-2

Q: Find f′(0), where f(x)= (x|x|)/(2+⌊x⌋)

A: Consider the given function fx=xx2+x

Q: F(x) = 2ln(x). What is F′(2)?

A: we have to find derivative of f(x) at x=2where f(x) is given by

Q: f(x) = Vxe-x/2 is inc decreacing

A:

Q: Can f(z) = | Re (z2) | + i.Im (-z) be derived from the function z=0? Show it.

A:

Q: (b) f(x)=2x +7atx =0

A: Answer

Q: Let f′(x)=√x−2 and suppose that f(9)=4. What is the value of the constant term in f(x)

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Q: 12x + 14 f(x)

A:

Q: Find f′​(x).   ​f(x)=5x−1         7x+9 f′​(x)=

A: The given function is fx=5x-17x+9 So, the value of f'(x)=df(x)dx Using the uv form of the…