1.Let  f(x)=cos(2x)+3x. Find (f-1)'(1).    2. Simplify the following expressions  a)log9(square root of 27) b) sin(2 cos-1 x) 3.  differentiate the following function  f(x)=x^2 x (tan x)^x

Q: 4. Determine the 75th derivative of each of the following functions. f(x) = 3 cos 2x b)

A: given function is f(x)=3cos(2x) we know d dx(cos(ax))=-asin(ax)  and d dx(sin(ax))=acos(ax)

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Q: 11. f(x) =log, 1+x

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

Q: 1) Find the derivative of y = e" tan x

A: As we know that; The chain rule; fgx'=f'gx·g'x And ddxex=exddxtanx=sec2x Given: y=etanx

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

Q: 7. Find the second derivative given g(x) = sin x² A. 2 (cos x² - x sin x²) C. 2x cos x² 9 "(x) - 4 x…

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Q: Find the derivative of each function. Show all your work and simplify the result completely.…

A: Since you have posted multiple questions, we will solve the first question for you. If you want any…

Q: Determine the derivative of the following exponential function d. f(x)= 10* (sin sin x)

A: We have to find the derivatives of the function.

Q: N or 8x 5 y 3= . 4x 2

A: Given function is y=8x+54x-2 To find derivative of the given function. Solution: Quotient rule of…

Q: 11. The derivative of cos 3x² is: a. -6x sin 3x² cos 3x² b. - sin 3x² c. -6x cos 3x² d. -6x sin 3x²…

A: Derivative represents the rate of change of a variable with respect to the independent variable. A…

Q: Find the derivative of: Y = 1098 (√x² +1-x)

A: given  y=log8x2+1-xwe know  (i)  logab=logaloga(ii)  d dx(logx)=1x(iii)  d dx(xn)=nxn-1

Q: find the inverse of the function f(x)=(3/2)cos(x/2)

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Q: dy for y =loge(l-Sin( 3x) Xア

A: We use chain rule to solve this differentiation

Q: a) Find the derivative of the following functions: i) f(x) = x Inx ii) f(x) = iii) f(x) = 1 4* iv)…

A: Solution:-

Q: 10. Use the exponential formula for coshx to find its derivative.

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Q: Example 2: Plot the function f(x)=cos3x below 0< <2

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Q: (a) f(x) = e (b) f(x) = tan(csc(x)) %3D (c) f(x) (d) f(x) [sin (6x)]*

A: Before solving the problem you must know some basic formulae.