a) Using the method of first principle find the derivative of the function 1 f(x) = Show that sin* x - cos* x = 1 sin? x – cos2 x -

Q: 1+sin 2 x 1) Find the derivative of f(x): 2 cos3 x

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: Use Theorem 1 to derive the formula.

A: Given  ddxsinx=cosxddxcosx=-sinx The trigonometric identity used here is  cot x=cosxsinxcosecx=1sinx…

Q: Find the derivative of the trigonometric function. y = 4x cos(x) + x2 sin(x) y' =

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Q: A-f cos (x)sin³(x)dx e*cosh (3x) B-J cosh(x)+sinh(x)

A: Here we use use substitution method to evaluate the given integral.

Q: Find the derivative of (b) f(x) = 2 tan-1(x) – 7x

A: Givenf(x)= 2 tan-1(x)-7x

Q: Find the first derivative of g(x) = 2 ln(x)tan(x*). 2 tan(4) g'(z) = | 82 sec²(4) In(z)+ X syntax…

A: We will solve the problem. The syntax error is ln(x4)  instead of 'CAPITAL i'. Refer to the final…

Q: Find an equation of the tangent line to the graph of the given function at the specified point. f(x)…

A: Consider the given function. fx=5excos x

Q: Find the second derivative of ƒ (z) = 6 sin (5z). Enclose arguments of functions in parentheses. For…

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Q: sin(z) Find the derivative of the funciton F(x) = In(1 + 6v) dv. F'(x) =

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Q: Find the derivative of R(y) 5 cos(y)-8 sin(y) (Use symbolic notation and fractions where needed.)

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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: Using the (limit) definition of derivative to show that the derivative of the function sin(x) is…

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Q: = * sin (t – 1) dt Find the derivative of the function g( x O sin (3x – 1) sin (2) 3 sin (3x – 1)

A: We will use Newton leibniz formula to solve this question.

Q: Calculate the derivative of y with respect to x. Express derivative in terms of x and y. esxy sin…

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Q: Find an equation of the tangent line at x = 0. y = x5 + cos(x) .13 (Use symbolic notation and…

A: We have given equation  y=x13+cosx Put x=0  y=0+cos(0)=1 Point on the curve x1,y1=0,1…

Q: calculate the derivative of y with respect to x. Express derivative in terms of x and y.…

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Q: 2л ind an equation of the tangent line to f(x) = 7 cos(x) at x = 3 Let y = f(x) and express the…

A: Given query is to find the equation of the tangent to the curve.

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: 4) Consider function sin(xy) =y a) Use implicit differentiation to find the derivative y'(x) at the…

A: sinxy=y a). Differentiating with respect to x, we get…

Q: 1. Calculate the derivative of f (x) = (sin (x) +2)®5 %3| showing all your work. 2. Calculate the…

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Q: The derivative of cos (x²) Graph y = -2x sin (x²) for –2 < x < 3. Then, on the same screen, graph…

A: We draw the graph of y=-2x*sin(x^2) using graphing calculator

Q: 3. Consider the function f (x) = sin² x + sin x on the interval (0,2n). a) Find the open interval on…

A: The given function is fx=sin2x+sinx on the interval 0,2π. a) Obtain the first derivative of the…

Q: (8) Find the derivative of the functions (i)h(x) = sin 2.x cos 2x (ii) f (x) = cos (tan 4.x) 1 =-…

A: We need to differentiate the given function. We will use different method of differentiation . ( As…

Q: Consider the function f(x) = cos(3 x). (a) Give the derivative of this function. f'(x) = | (b) Find…

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Q: 4. The 1" derivative of y : cotx a) xsec?x + tanx b) xsecx - tanx c) cot x + xcsc'x d) cot x - xcscx

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Q: 2. Find the derivatives of the folowing equations: y = sin-'(1 -t) y = csc-(x/2) y = In(tan- x)

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: 1+sin 2 x 1) Find the derivative of f(x) 2 cos3 x

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Q: 3) (a) Let f(x) = -x²-x. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

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Q: Find the derivative of the given. f(x)= cos x cot x let g= cos x and h= cot x. Then, g'= -sin x…

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Q: f(x) = -3 sin(x) cos(x)

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Q: Compute the derivative of the function y = 6 sin¯'(x) at the point x = . CUse symbolic notation and…

A: Topic = Derivative

Q: Find the second derivatives of f(x) = 2x2+3x  3x+5

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find the derivative of these functions with respect to x. In(sin-1(x))

A: Given query is to find the derivative of the expression.

Q: C. Find the derivative of each function. x' - 2x 3. h(x) = 4. F(x)=sin x- cos x- tan x tan x D.…

A: Follow next step

Q: Calculate the derivative of y with respect to x. Express derivative in terms of x and y. e5xy = sin…

A: Given query is to find the derivative of the expression.

Q: 12. Find the first derivative of y = 2cos(2 + x*). A. -4x sin (2 + x2) B. 4x cos (2 + x*) C. x sin…

A: Questiopn no. 12,Given,           y=2cos2+x2To find : The first derivative of the function.

Q: Find the derivative y = (2 – x²) cos x + 2x · sinx 2 sin x – sin x (2 – x²) 2 cos x – sin x (2 – x²)…

A: Differentiate wrt x

Q: a sin (cos X) b cos (cos x) c sin (sin x) d cos (sin x) a By expressingy = x in the form y = sin…

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Q: y = cot2 sin ( Tan-1

A: follow next step

Q: 1. Use logarithmic differentiation to find the derivative of the function. y = x4 cos(x) 2. Use…

A: Here we have to find the derivative of the given functions using logarithmic differenciation.

Q: a) Use the definition of hyperbolic functions to prove the identity 1-tanh2 (2x)=sech2 (2x). b) Use…

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Q: Find the equation of the tangent line to f(x) 16e* cos2(x) at x 4 (Use symbolic notation and…

A: To determine the equation of the tangent line.

Q: the slope of the tangent. line to: the graph of y=XT COSXY the point (0,1)? What is of: 4=XT COSメ

A: Given: y=x+cosxy

Q: calculate the derivative of y with respect to x. express derivate in terms of x and y.…

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Q: 1 f(x) = sin(x) – sin(3x) + sin(5x), [0, x] (a) Find the first and second derivatives of the…

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: 3) Find the derivative of the functions. Make sure to show all work, and explain which…

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Q: Find the x-coordinate of all points on the curve y = sin(2x) + 2 sin(x) at which the tangent line is…

A: Determine the derivative for y. y=sin2x+2sinxy'=ddxsin2x+2sinxy'=ddxsin2x+ddx2sinxy'=2cos2x+2cosx

Q: ∫(3 cos(x) − 7sinx(x))dx   Evaluate indefinite anti-differentiation

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Q: Find the indicated derivative. Find y " if y = 5x sin x. O y" = - 5x sin x y"= - 10 cos x+ 5x sin x…

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