Find f'(x) given トhat fcx)= tan Cax - Jx +4ょ3) %3D (assume real number) is

Q: 4) Estimate tan (0.5) using the tangent line to y = tan(x) %3D 6

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Q: Find the relative extrema using both First and Second Partial Derivative test f(x) = Sin2x ; 0<x<n

A: i) The given function is fx=sin2x. Given that the domain of the function is 0,π. Obtain the first…

Q: dy Use implicit differentiation by partial derivative to solve for of function 3x2 + 2xy = -4y³. dx

A: Given that: 3x2 +2xy = -4y3. Find dy/dx. We know that derivative of xn is nxn-1.   Here i attached…

Q: Explain the method of proving the derivative (dy/dx) of sinh(x) and cosh(x) ?

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Q: ind y' by implicit differentiation: xy3 - sqrt (x2 +1)=2y

A: Definition used -    Implicit differentiation-  If equations do not define explicitly y as a…

Q: Find the derivative of the function. rsin(x) y = In(1 + 5v) dv y'(x) = sin x In(1+5 cos x) + cos x…

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Q: Use forward, backward and central difference to estimate the first derivative of f (x) = In at x =…

A: Given function is fx=lnx and x=3 Step size h=0.01 We have to estimate the first derivative of fx=lnx…

Q: Find the derivative of f(x, y) = xey + cosxy at the point (2,0) in the ection.

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: Find the derivative of the function. 2x F(x) = arctan(t) dt 1 2 arctan(2x) F'(x) = (arctan(Vx)) -

A: Here we have,

Q: 2.) Compute for the derivative (DO NOT USE THE DEFINITION) of A. 2x3 y = tanh sin x2

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Q: Xyz. %3D Use implicit differentiation to find az/ar

A: The given function is ez=xyz.

Q: The total derivative of f(x,y) = ylnx  is

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Q: Estimate the derivative of f(x) = sin x at x = π/6.

A: Given,       f(x) = sin x at x=π6

Q: Estimate the root very near x = 0.4 of 4(x*)" - 4(x²) + 1 = 0 using the Newton- Raphson Method with…

A: Consider a function:  fx=4xx4-4x2x+1      =4x4x-4x2x+1

Q: What is the derivative of cosh-1(xy) + elog x = sec3(y2)

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Q: Use forward difference approximation to estimate the first derivative of the following equation.…

A: Given that, fx=-0.15x3-0.2x2-0.5x+2.25h=0.5We need to find the first derivative of the function at…

Q: Evaluate the derivative of y = sin'6x + In /1- 36x, where x= 0.125. dx |x= 0.125 U (Type an integer…

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Q: Find the derivative of y with respect to x if y=∫0ln(3x) sin(6et )dt

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Q: Use forward, backward and central difference to estimate the first derivative of f(x) = In(x) at x =…

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Q: What is the connection of the concept of limits to slope to derivatives (delta method to simple…

A: The limits of the function at a point are calculated using the formula . The limits are used to…

Q: Find the derivatives of the functions in Exercis

A: fθ=sinθ1+cosθ2

Q: Find a function that has x^6 as its derivative without using integral knowlegde.

A: In this question, we need to find a function that has x6 as its derivative.

Q: Calculate the derivative of y=arctan√ex at x=0.

A: We differentiate both sides with respect to x using the chain rule.

Q: Is the function f(x) = |x| cos x differentiable at the point x = 0 ? (Use definition of the…

A: if lim∆x→0f(∆x+x)-f(x)∆x doesn't exist then not differential

Q: The derivative of the function y = etan(4x) is: a) y' = tan (4x)etan(4x) b) y' = 4 sec²(4x) etan(4x)…

A: Given data: The given function is y=etan(4x). Differentiate the given expression with respect to x.…

Q: What is the derivative of f(x)=−cos(x)+4sin(x) at the point x=−π/2?

A: We will find the derivative as following.

Q: Is the functionf(x) = |x| cosx differentiable at the point x =0 ? (Use definition of the derivative)…

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Q: Consider f(x) = 3 − cosx on the interval [0, 7]. When will the first derivative equal zero?

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Q: The second derivative of y = ln(sec x) is а) у 1 - tan x b) y = tanx sec x c) y = secx · tan x d) y"…

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Q: Let f(x, y) = cos(x+y²). Compute the rate of change in the direction of fastest increase for f at…

A: Find gradient and its magnitude then solve

Q: Find by implicit differentiation when ry sec(y) 1+y* 3 -

A: The given equation is:xy3secy-3=1+y4

Q: Find the equation of line tangent of sin(2x) cos(3x)+ sec(x) TC At x = 6. %3D

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Q: Compute the equation of the tangent line to f (x) = sin(Tx) at x=0.5.

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Q: 9. For f(x) = arctan (2 sin ( Vx )) , compute the first derivative at the point %3D X =

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Q: What is the derivative of f(x)=2sin(x) at the point x=−π/2?

A: To find the derivative of fx=2 sinx, at the point x=-π2.

Q: Find all x values in interval [0,2 ·¤] on the graph of f(x) = -3·sin(x)·cos(x) where the tangent…

A: Given,            f(x) = -3 sin(x) cos(x)

Q: 1 m' (x) = x In(x)

A: Given: m'x=1xlnx for finding anti-derivative of given expression, we substitute lnx=u…

Q: A piece of wire, 370 cm long, is to be bent into an isosceles triangle. What should the exact…

A: given: A piece of wire, 370 cm long, is bent into an isosceles triangle. we have to determine what…

Q: Show that the function has partial derivative at the point (0,0) but is discontinuous at this point.

A: solve the following

Q: What is the second derivative of y + Incosx = 0 * O (cos x) ^2 O 1 O (sec x)^2 tan x

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Q: dy Find by implicit differentiation. dx ху — ху" %3 8 -

A: Implicit differentiation: Differentiate both sides of an equation with two variables by considering…

Q: Calculate the derivative: d/dt ∫ from 1 to tan(t) of sin(x^2)dx=

A: Here the function is of the form:

Q: The derivative of y=esinh/x + coshVx equals Select one: 1 1 (esinh/cosh/x + Vx² -1 2х 1 O y' = e…

A: We have to solve

Q: Find the derivative of the function. 5/1 x+1 In 22 + arctan x %3D X -1· dy dx

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Q: Using the đết of derivative, fin rivative of f(x) = x² + 2x + 2.

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Q: /1 – ť dt dx cos X

A: This is a basic calculus question

Q: Find the most general antiderivative. Verify with differentiation f(x)=cosx + 2sec^2x

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Q: Find the derivative of s(*) - L Int dt 1+t

A: