COS . Answer the following questions f(x) 3 and f'( Suppose that f() 5, and let g(r) f(x)sinr and h(x) Find g'(T/4)

Q: Find for the following function. dx 6 cos x y = 6-5 cos x dx

A: To find the derivative of y.

Q: What is the equation of the line tangent to the curve e" + cos(x) = 1 at the point C.0. y =1- ... A…

A: Given; ey+cosx=1 at point (π/2,0).

Q: (a) Find dy/dx for 3 tan x – In x x2 (b) Find f"(x) for the following function: e" In(x**) f(x) = x…

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Q: Let z be defined implicitly as a function of x and y by the equation dz 4+ In (xy²) – cos (xy – 2) =…

A: Given: Let z be defined implicitly as a function of x and y by the…

Q: 11.Determine the equation of the curve whose tangent line at any point (xy) is e* – sin x and passes…

A: Given problem:- Determine the equation of the curve whose tangent line at any point (x,y) is ex -sin…

Q: Let f(x) = cx + In(cos(x)). For what value of c is f'(T/4) = 5? %3D

A: Given: f(x)=cx+log(cos(x))  and f'π4=5 find values c

Q: Suppose f and f' are differentiable functions of r. Given f' () = 0, f" () -1, and g(x) = log…

A: Differentiate two times at given value

Q: * 3x ], the x-coordinates of the points on the graph of the function f(x) = 1 + cos x where the…

A: For horizontal  tangent dy/dx=0

Q: Find for the following function. dx 5 cos x y= 6-7 cos x dx

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Q: For the function f(x,y)= (x² + y²) tan(ln(xy)) + e(x-y) which of the following is the value of…

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Q: Consider the following function and express the relationship between a small change in x and the…

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Q: (2 – 4t) sin() tan(2r) V17 – cos(2nt) Find the equation of the line tangent to the graph of f at r =…

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Q: cos='A F'A where A =atib

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Q: Compute the derivative d/dx of the following functions: y = 2 sec x − csc x x cos^2(4x)…

A: y = 2 sec x − csc xDifferentiate w.r.t.xdydx=ddx( 2 sec x − csc…

Q: 3. Find the derivatives of each of the following functions. (a) g(x) = (tan x)³ (b) f(t) = arctan(t)…

A: Topic: derivative

Q: Find the derivative of the following function. y = In (x° +6)" dy %3D dx (Type an exact answer,…

A: Given: y=ln(x3+6)π To find the dydx=?

Q: Consider the following function and express the relationship between a small change in x and the…

A: Givenf(x)=10-acosxwhere a is constant

Q: Suppose f and f' are differentiable functions of r. Given f' () = 0, s" (÷) = -1, and g(r) = log…

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Q: . Suppose y is a function of x defined implicitly by sin y + y = x²y² + In(x) – 1 Find dy/dx and…

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Q: of dx- = 0, then dy |=0. Prove that is a function f is harmonic

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Q: O Find the derivative of the g f X COsy = ya sinx followny %3D 4) (2x+3y)"= e" tany %3D () sin xty)…

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Q: Find G(1), G'(0), and G'(π/4), where G(x) =

A: Here we have;  G(x)=∫1xtant dt

Q: Q5: Find for the following functions: (1) In(x - y) = xy + y³ (2)y=tan³ √/cot(7x); (4) y = x sinh…

A: Solution is given below:

Q: dz (2) Suppose z is a function of x and and suppose cos(32) xyz?. Find in Y, terms of x, y, and z.

A: The given function is, cos3z=xyz2

Q: find the aradients of the functions below a)f(x, y) = e-3y cos4x

A: We have to find

Q: 2. Consider the squiggly graph of all points (r, y) that satisfy sin(re") = a + y. 1 Using implicit…

A: Given, sinxey=x+y

Q: 3. Find the derivative of each of the following functions. Justify your answer. I sin z (a) f(x) =…

A: As we know that; The Product rule: f·g'=f'·g+f·g' The Chain rule: fgx'=f'gx·g'x   And…

Q: - cos (3.xz) = 5 defines z as a function of x and y. Differentiate implicitly to Assuming y az find…

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Q: 1. b. Find the differentiation of the following functions: i. y = 2 tan(1 – 2x) + ex²+x -

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Q: Find the values of x between 0 and 2n, if any, where the graph of y(x) = sin(x) cos(x) has a…

A: Given : yx = sinxcosx

Q: I Find the second derivative(y") of the following functions and simplify the final results. 4. y =…

A: 4 y = xcosx now fist derivative y' = x(cosx-1)cosx(-sinx) y' = (-1/2)sin2x x(cosx-1) now again…

Q: What is the equation of the line tangent to the curve e+cos(x) =1 at the point ,02 + cos Ay= y=x-…

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Q: Differentiate the following function. y= sin° x dy 4. 5 sin " (x) cos (x) dx

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Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = 4

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Q: 1. b. Find the differentiation of the following functions: i. y = 2 tan(1 – 2x) + e*²+x ii. y =…

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Q: Find for the following function. dx 3- cos X y = 4 + coS X

A: follow next styep

Q: b. Find the first and second order derivatives of the following function: In(Tx) y = sin(Tx + 3) *…

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Q: Given that f(x, y) - cos(x²) + 6e* sin y . Find fxyxyx · %3D

A: fx, y=x61+6y-cosx2+6exsiny Partially differentiating with respect to x, we get…

Q: 9) For the defined function, give the a applicable. y = -÷+ cos (3x +).

A: Given Data The function is y=(-5/2)+cos(3x+π/2).   The general equation of cosine function with…

Q: Find the slope of the tangent line to the path of a carnival ride x 7 cos() + sin(7t), y = 7 sin() +…

A: Given  x=7cos(t)+sin(7t) y=7sin(t)+cos(7t) We need to find the slope of tangent at t=0

Q: (b) Find the derivative of the following functions with respect tox. (i) y = sin (2x – 3) (ii) y = x…

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Q: Find the derivative of the following function. y= In (x +8)* dy dx (Type an exact answer, using x as…

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Q: Q2) Find the derivative of the function at Po in the directi g(x, y) = x – (y²/x) + V3 sec-' (2xy),…

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Q: For sin y=- find the value of so that (y+y")= - 1 at 1 at x=0 Cos X-

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Q: 1. Determine the relative extrema of the function y = 2 cos x + sin 2x on the interval (0, 2Tt). %3D

A: To find the extrema of the function

Q: a² f For the function ƒ(x,y), compute Or d0 if x =r cos O and x=r sin 0 .

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Q: I Find the second derivative(y") of the following functions and simplify the final results. 1. y = x…

A: Product  Rule of differentiation: du.vdx = u.dvdx +dudx.v dcos(x)dx = -sin(x) dsin(x)dx = cos(x)…

Q: Let  f(x) = cx + ln(cos(x)).  For what value of c is  f '(π/4) = 9?

A: Consider the given function, fx=cx+lncosx first differentiate the function using chain rule as…

Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Equation of tangent line through A(x1 , y1) is given by :- y – y1 = slope x (x – x1)

Q: H.W Ex.(8) Show that the functions f(x) = sin' () and ga)=2 tanv メ+) have the Same derivative.

A: