The derivative of any constant is 0. The well-remembered triq identity tells us that sin2(x) + cos2(x) = 1 is a constant. Verify that sin2(x) +  cos2(x) is a constant by showing, with the product rule, that its derivative is indeed equal to 0.

Q: Find the first derivative of 2cos(2 + x³). a. -6x² sin(2 + x³) b. -x² (sin 2 + x³) c. -6x² (cos…

A: daf(x)dx=adf(x)dx ; where , 'a' is constant. dcos (ax)dx =-a.sin(ax) dxndx=n.xn-1 .

Q: Find and simplify the second derivative of f(0) = cos(sin(30))

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Q: Find the actual error when the first derivative of f(x) = sin(2x) at x = 1/8 is approximated by the…

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Q: Find the derivative of g(x) = In(sin²(ed/x)).

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Q: , Suppose that the tangent line to the graph of f(x) = xlb) at r = 1 is equal to the tangent line to…

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Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = (2…

A: Given function is   Differentiating both sides with respect to x, we get

Q: The derivative of the given function is cos x sin x

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Q: Find the second derivative of the following  a .) 2x^3- 1/2x b.) Cos(x^2)

A: The given functions are  a) 2x3 - 1/(2x) b) cos(x2)

Q: -1 We can conclude from the derivative of sin-1(x)and cos-1(x) that sin-(x) + cos¯(x) is constant.…

A: Explanation: find the derivative of sin-1x & cos-1x

Q: Find the derivative of the following. y = -1/3tan3 x - sin2(2x)/tan x - cos2(2x) cot x +4

A: Differentiation of the function can be found with the help of the differentiation formula.…

Q: Compute the derivative of the following function and find its tangent line at x = 0. Graph the…

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Q: The derivative of In (cos x) is

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Q: Consider the function f(x) whose second derivative is f''(x) = 4x + 6 sin(x). If f(0) = 3 and f'(0)…

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Q: 43. Use the identity cos 2x = cos x cos x - sin x sin x to find the derivative of cos 2.x. Express…

A: cos2x=cosxcosx-sinxsinx find the derivative of cos2x So here use product rule and then find…

Q: Consider the function f(x) whose second derivative is f''(x) = 3x + 8 sin(x). If f(0) = 4 and f'(0)…

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Q: 3. Compute 4 (sin? x + cos? x) without using the derivative formulas for sin x and cos x.

A: Given:

Q: Find the derivative of y with respect to 0. y= 30( sin (In (30)) + cos ( In (30))) de (Use…

A: topic- derivative of a function

Q: 7. The derivatives of the function f (x) = cos(3x²) that follow are incorrect. What misconception…

A: The differentiation of product two functions can be calculated by using the formula,…

Q: Find the derivative with respect to the independent variable. f(x) = 9 cos x - 2 sin x f'(x) = D %3D

A: We have to find derivatives of function: fx=9cosx-2sinx We know the derivatives of trigonometric…

Q: Obtain the derivative formulas for csch x, sech x, and coth x from the derivative formulas for sinh…

A: Given functions are sinhx,coshx,tanhx.

Q: What is the derivative of cos2t

A: Formulas used

Q: 4) a) Determine the simplified expression for the 623rd derivative for the function f(x) =cos(2x)…

A: a)   fx=cos2x+sin2π     =cos2x+0      = cos2x

Q: What is the derivative of sin? x f(x) = with respect to x? COs x

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Q: Suppose that the tangent line to the graph of f(x) = x0") at x = 1 is equal to the tangent line to…

A: topic:- application of derivatives

Q: 1. Find the derivative of the following sin² x cos² x a)y + 1+cotx 1+tan x

A: We have to find derivative of given trigonometric term.

Q: Which of the following functions have a 4th derivative different from itself? ex sin x CoS X

A: In this question, we need to find which of the given functions have a 4th derivative different from…

Q: The derivatives of sin- 1 x and cos- 1 x are negatives of each other.

A: From the question it's not clear, what do you want us to do with it. I assume that you want to know…

Q: 4x3 ソ= cos sin e2x

A: We have to simplify the derivative

Q: use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y =…

A: given y=cos9θ+41

Q: f (x) = cos-(sin(x² + 3х))

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Q: Find the first derivative of y = cos4 x – sin4 x and y = x3   –  x2 cos x  +  2x sin x  + 2 cos x…

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Q: Find the first derivative Complete Solution.  1.) t=sinθtanθ

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Q: Find the second derivative of f (z) = 6 sin (5z). %3D Enclose arguments of functions in parentheses.…

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Q: Solve for the derivative of the following trigonometric functions. 1. f(x) = e3x 2. f(x) = x³ ex 3.…

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Q: Find the equation of the line tangent to the graph of f(x) = -2 sin (x) – 1 at'x = =. (Enter an…

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Q: Find the second derivative of f (x) = 9 sin (2æ). Enclose arguments of functions in parentheses. For…

A: Second derivative of f(x) is given below...

Q: Given: f(x) = 1– sin² 4x . find the 5th derivative

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Q: Use a central difference method to approximate the first derivative of cos(x) at x = pi/3., assume…

A: To approximate the first derivative of fx=cosx at x=π3 by taking the value of h=0.01.

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

A: see the details solution in below

Q: (A) Find the first derivative of the following function: 1+ cos2x f(x) = %3D 1- cos2x |

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Q: Find the second derivative of f (z) = 6 sin (4z). %3D Enclose arguments of functions in parentheses.…

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Q: The derivative of y = 3 cos (V1- x²) + (1-x²) 2 can be written as 3 1–x² sin ( /1-x² ) - (1-x² ) 3x…

A: This can be done as follows:

Q: [sinhc(x + 7)| In(x- 4x + 13) + sin(x) b. dx

A: We have to find

Q: Consider the function f(x) whose second derivative is f''(x) = 10x + 8 sin(x). If f(0) = 3 and f'(0)…

A: Given, f''(x)=10x+8sinx(x) After integrating the above equation,…

Q: f(x) = (x + 6 sin x) (1 – 5 cos x -

A: To find the derivative of:f(x)=x+6sinx1-5cosx

Q: Use the theorems on derivatives to find the derivative of the following function:   y = (cos(x))2 +…

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Q: 3. It is given that sin(x) + cos(x) tan(y) = 1. Use implicit differentiation to find

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Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 10 sin(x). If f(0) = 3 and f'(0)…

A: Given function is f"(x) = 9x + 10sin(x)

Q: What is the derivative sin?x+cos?x

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