what is the deivative oF: tan(3x) eX y = In x

Q: If sin' 0+y cos e sin e cos e and x sin e = y cos 6, prove that x + y* = 1.

A: Solution

Q: The value of 1 cos (tan ¹y) + y sin (tan¯¹y) cot (sin¯¹y) + tan (sin¯¹y) is......... +y¹

A:

Q: Eliminate n from their equations  X= sin n + tan n and y=sin n - tan n

A: With the help of trigonometric identities we eliminate n from the equations.

Q: tan e de (1+ In cos ele

A:

Q: Show that (i) tan x < x, 0<x<T/2

A: In this question, the concept of Trigonometric Function is applied. Trigonometric Function The…

Q: 4. Evaluate sin (x) cos°(x)dx

A: To evaluate the integral

Q: 5) Evaluate the integral: tan 3 x dx

A: Given integral, ∫tan3x dx

Q: 1 Differentiate y = tan 8x + cos ,x

A: Using differentiation rule,

Q: 4. Evaluate 5 cos x dx 3 v2 sin x – 1

A: To evaluate : ∫π6π3 5 cos x32 sin x - 1 dx

Q: 3x 7 If sin x= - 西,1Sx<2 37 and CoS y = 2 evaluate: tan (x+y)

A: Given problem:-

Q: Establish the identity. sin x+ sin y X+y = tan COS X+ COs y 2.

A:

Q: find integral tan 3 x dx

A: To find the integral of tan2x first split tan into two part and the using property of sec and tan…

Q: 5. If y= tan x, prove that y``=2(1+ y² )(3+ y²).

A: Prove the given equation

Q: 1. fcosax tan(sin ax)dx - In |cos(sin ax)|+ c ans : or In |sec(sin ax)| + c 2. Ssin(cos.x)·sin x dx…

A: Here we use the other formulas with the given one and also use substitution.

Q: 1. If Y= 4 In (In (In(sec(x)) then Ý=[4 (tan)/{ In ((In (sec)) In (sex)}]

A:

Q: 2x, given tan x= 2 and cos x is less than 0

A: Given tan x = 2 and cos x &lt; 0.

Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

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

Q: If f(x) = COS X then f' (x) equals: X S0)- -sin x cos X:

A:

Q: 1. Solve the DE tan x sin y v + ( 3tan X -2 cos y) sec'x=0

A:

Q: 4. What is (Cos (x²)} dv 5. What is (tan x³) dx 6. What is (In x)7 dx

A: To find out the derivative.

Q: 1. What is S tan x dx?

A: log|sec x|+c .

Q: Evaluate (tan x cos x) dx А. cos x + C cos x + C - С. - sin x + C D. sin x + C B.

A:

Q: Solve using the false rule method f(x) = /x² + 1 – tan x %3D starting at the interval [0.5,1]

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Q: 5. | sin (Tx) cos (Tx) dx

A:

Q: Show that the two formulas are equivalent                                                      ∫tan…

A: To show that ∫tanx dx=-lncosx+C and ∫tanx dx=lnsecx+C both formula are equivalent. We know that…

Q: IFS(x) = - sin(x), then S ® (1) is equal to - sin(x) B) - cos(x) sin(x) O cos(x)

A: We have to solve

Q: 2. Find a reduction formula for sin" x dx. By using this formula evaluate sin® x dx.

A: The objective of the question is determine the integral.

Q: What is the antiderivative of -tan(x) + pi^x?

A:

Q: /3 dx cos x tan x /4

A:

Q: 4) If y = 2√x - 2 tan-¹ √x, then y y' = -1 1+x²

A: Given :y=2x-2tan-1x

Q: 21. y = csc 2x 22. y = tan 2 Vx* + 1 x tan x 24. y 23. у x? + 1 1 + sin? x

A:

Q: If 4 f(x) = %3D 1+ sin x then 4 cos x f'(x) = (1 + sin x)²

A:

Q: Evaluate ex sin x dx. A - ex (cos x + sin x) + C В e* (cos x + sin x) + C C) -ex (sin x - cos x) + C…

A: We will find out the required solution.

Q: (9) ſ cos(x²) 2xdx sin x? + c cos x2 + c Option 1 Option 2 sin 2x + c

A: We will substitute  x2 = t

Q: find do diy y = (cos(x))*os)

A: Given y=(cos(x))^(cosx) Now differentiate y with respect to x

Q: Compute (sin (x)) dx cos'x 3 sin' x cos x O Not listed here 3 sin? x 3 sin x cos x

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

Q: the integral of tan^2 (x) cos^3 (x)dx

A: To evaluate the given trigonometric integral

Q: Find if dy dx y = (cos x) * O (cos x) * (-sin x) O (sin x) * (In cos x - x tan x) O (sin x)* (In cos…

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Q: If y=(1+x²) tan-x - x then y' is equal to

A:

Q: 3) If y = sin(2n), and x = cos(2n)

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: If f(x) 3 tan-'(3 sin(3x)), f'(z) =

A:

Q: If x is measured in degrees and f(x) = cosx, then d f(x) = − sinx

A: To write that it is true or not.

Q: = 2. If y = sin³ (-) cos³ (1) prove that y' = sin² (x) cos(x)

A: Topic = Derivative

Q: 9. Prove that | sin n0/sin 0| <n, limiting values being used when sin e = 0.

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Q: 1 Integrate: S tan*÷x dx 3

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Q: What is q'(x) when q(x)=ln((5x^2+x+7)/((x^2/3)(sin(x)))

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Q: a) y=In(*). x tane 4 cos x y = 3x + sinx b)

A: Given: The functions are, a) y = ln ( x tan ex )

Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3

A:

Q: 04.) Show that y = (sin x +cos x) sec x = sec² x

A: Given inequality does not equal. See the attachment