4. Consider the functions fand g whose graphs are given below. Find the following derivatives 7 y = f(x) y = g(x) а. f(2) b. g'(2) с. f(2) d. g(2) f (x) dx g(x)+ f(x), d е. when x = 2 d f. -(({(g(x))), when x= 6 dx

Q: Find the derivative of function.

A: Find the derivative of function. y=(ln|x+1|)4

Q: 5. Find the derivative of: a. f(x) = cos(e³x-4)

A:

Q: Find the derivative of function.

A: The given function is f(x) = ln(xex+2).We have to find the derivative of this function with respect…

Q: Find the derivative. h(x) = In(cosh(7x)) h'(x) =

A:

Q: 4. Calculate the derivative of the given function directly from the definition of derivative y = v2x…

A: Given function is  y=√(2x+1)

Q: 17) Find the first derivative of f(x) = (cos4x)6 6 or f(x) = cos 4x

A:

Q: Calculate the derivative of the following function. 7 y = sin '(cos (3x)) If the Chain Rule only…

A: To find the derivative

Q: 2.) Investigate the derivate of the function ƒ(2)=Imz by using definiton of derivative.

A:

Q: Suppose the derivative of the function y = f(x) is y' = (x- 2) (x + 6). At what points, if any, does…

A: see 2nd step

Q: 1 Find the first derivative given that f(x) = xdx +

A:

Q: 2 The derivative of (g(x))¯ is equal to (g '(x))¯. Select one: True False

A:

Q: Sketch the graph of a function z = f(x, y) whose derivative fx is always negative and whose…

A: Given that z=f(x, y) fx is always negativefy is always positive

Q: FInd the derivatives of the function f(x) from the first pribnciple  cos2x

A: Derivative from first principal is ratio of change in y to the very small chance in x.

Q: 10) Find the second derivative of k(z) = 4 cscz.

A: Given: kz=4cosecz for finding second derivative of given function, we find first derivative then…

Q: 2х Find the second orfer derivatives of y=Tan" 1-x3

A:

Q: Find a function y=f(x) whose second derivative is y''=12x-2 at each point (x,y) on its graph y=-x+5…

A: The second derivative of the function, y and tangent to the graph of y is given as,

Q: 2. Find the derivative of y= ecos{/x+3) Solution:

A: Topic:- derivatives Note:- as per our guideline if more than one question uploaded than only first…

Q: 8. Find the derivative of the function. y= In(1+x)

A:

Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = π/4 , g'(2) = 5, and g"(2)…

A: singx

Q: 10)Find the first derivative or f’(x) of the following functions using long method derivatives

A: We need to find derivative of given function.

Q: Compute the derivatives of the given functions. f(x) = 5 ln x   f'(x)= ? g(x)= ln (x^5). g'(x)= ?

A:

Q: 1 14) Use the definition of derivative to find dx 3- х.

A:

Q: 6. Find the first order derivative with respect to z of the function u = In/x2 + y2 +z²

A:

Q: Find the first derivative of y = 1 using the Chain Rule. (1– x4)6

A: These questions are related to differentiation, We will solve them using given information.

Q: 5. Find the derivative of y = In(cos v3x + 2 ), by using chain Rule.

A:

Q: 1) Find the second derivative of f(x)= 24\x . (6) 2) If y = cos x, what is y (x)?

A: To find the derivatives of the given functions.

Q: (6) Find the derivative where it exists (c) Where is flz) analytic ?

A:

Q: Compute the derivative of the function y = 6 cos- (7x) at the point x = (Use symbolic notation and…

A:

Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

A: The objective is to explain the reason definition of numerical derivative doesn't exist at x=2 in…

Q: 22 Find the 43rd derivative of (1 + x²)“ at x = 0. 0.

A:

Q: 7. Find the nth derivative of y = 1//x.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 4. Find the first derivative of y = 170x tan (20x)+- In(49 – x 5e7-8cos

A:

Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = 4, 8'(2) = 5, and g"(2) =…

A: Given: The function singx with g2=π4, g'2=5, and g''2=3, To find: The second derivative of given…

Q: Calculate the derivative of the following function. y= sin (cos (3x)) If the Chain Rule only needs…

A: In the question we have to find derivative of the given function.

Q: Calculate the first derivatives of ƒ(x) = x2/(x2 + 1) and g(x) = -1/(x2 + 1). What can you conclude…

A:

Q: 1) Find the derivative. Simplify where possible. y = x tanh-1x + In/1 – x²

A:

Q: Find the derivatives of the functions defined as . y = cos4 x

A: Given function, y = cos4 x

Q: 5. Find the derivative of the following. 3x-5 а. у3 b. y = In (sin(3x-5)) c. y= e2x arc tan (2x + 3)…

A: Explanation of the answer is as follows

Q: 4) Find the derivative of y = arctan(x² + 3)

A:

Q: Find the derivatives of the functions defined as y = ecos x

A: Derivative of ex=ex Derivative of cos x =-sin x

Q: 15 - What is the approximate derivative of f(x) = 5x³ + 4x² if we use f(ze+h)–f(za) forward…

A:

Q: 3. If the derivatives of h with respect to U; for h=²u

A:

Q: Find the derivative of f (x) =arcoth (e³" ).

A:

Q: -5

A:

Q: Obtain the derivative of the function y (ctg(5x))} y =- - sen? (5x) + 1

A:

Q: 2. Determine the 8th derivative of y with respect to x of the function f(x) = 1 + x2 and find the…

A: fx=11+x2 Differentiate the above function with respect to x. f'x=ddx11+x2=2x1+x22 Again,…

Q: Find the first derivative of h(x) if h(x) = cos (x – 2x) -

A: h(x) = cos2(x3-2x)

Q: Suppose that the first derivative of y = ƒ(x) is y′ = 6(x + 1)(x - 2)2. At what points, if any, does…

A: To determine if the function has any points of maxima, minima or inflection, use second derivative…

Q: Find the derivative of the function. h(x) = ets. - x + 1

A: Differentiate w.r.t x