We have determined that g'(x) = 2 and h'(x) = cos(x), where g(x) = 2 In(x) and h(x) = sin(x). Applying the Chain Rule, gives the following result. F(x) = h(g(x)) F'(x) = h'(g(x)) · g'(x) 4 sin(In(x²)) – 2 cos(In(G²))

Q: f(x) = (2x3 tan(x) – e-*)10 and g(x) = /(3x – 4)² – sin(x). %3D %3D

A: We have to use the chain rule to find the derivatives of f(x) and g(x)   We also have to find…

Q: ) = 5 + 4 sin(x). If f(0) = 3 and f' (0) = 4, what is f(x)? Consider the function f(x) whose second…

A: Given:

Q: Letf (x) be defined by f (x) x sin(-) for x # 0 and f (0) = 0. Find f' (0). O 1 Does not exist.

A: Please refer to the image below

Q: b) f(x) = cos(x)

A: To find the derivative using the chain rule. fx=cos2x

Q: if f(2) = 1, f'(2) = 3, g(2) = 3, and g'(2) = -1, then the derivative of f(x).g(x) evaluated at x =…

A: Given: f(2) = 1, f'(2) = 3, g(2) = 3, and g'(2) = -1

Q: Let y = (x + sin(x))³. Find g(æ) and f(x) so that y = (f o g)(x), and compute the derivative using…

A:

Q: If f(x) = 15 to dt then f'(x) =

A: Note:-Since you asked multiple questions according to our policy we can answer only first question…

Q: f(x) = sin(sin()) then f' (x) =

A:

Q: 2. Let f(x) = cos(x). We will take derivatives of this function over and over. (a) Evaluate the…

A: Using standard formula of derivatives.

Q: Differentiate the function. f(x) = sin(x) In(3x) sin (x) f '(x) + cos (x) In (3x)

A:

Q: Write the given expression in an expanded form. Assume that variables represent positive numbers.…

A: Given, lnxx3-7x2+9   We have to write the above expression in expanded form.

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.