dy is let y = (sin æ)*tan z then dx %3D :Select one (sin æ)tan z [1+ sin² x ln(sin æ)] .a (sin æ)tan z [1+ sec² æ ln(cos x)] .b (sin æ)*an z [1 + sec² æ In(sin æ)] .c (sin æ)tan z [1 + sec æ In(sin æ)] .d

Q: Find dy/dx for the following : 1) y = x3 + sin x² + sin-1 5x 2) y = 32x + In (sin x²) + In(sin-1 5x)…

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Q: Si sin“ (3y) cos® (3y) dy 128 2340135 128 780045 O 9.64 x 10 4 O 2.89 x 10 3

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Q: dy Find for y = tan-(3z) de Ans=

A: A detailed solution is given below.

Q: dy evaluate dx (sinx+1) 5-1f: y = (cosr+1)

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Q: x sin wx O Show that dx = x² + 6x + 10 (3 sin 3w + cos 3w) w> 0

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Q: ) Evaluate A) /16 /2 cos (167 x5 ) dx dy. Os xs 2 Og y s x*

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Q: The approximation of I = = co cos (x²+5) dx using simple Simpson's rule is:

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Q: To evaluate 3cos x=1 dr. the integrand can be transformed to 1-sin2x A.) S(3cos³x + csc?x)dx B.) 3…

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Q: B: 3:Use Gamma & Beta properties to evaluate : f (In x) 3 dx

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Q: ди 1. find аnd az if z = 5 tan(x)and x = e" + In(v) at the point (In2, пр dv dy 2.Find if, y2 + x² =…

A: 1. Given,               z=5tan-1(x)       and  x=eu+ln(v)

Q: Find dy if g-s(tant). and t= CostX)

A: Given functions,  y = sin (tan t) t = cos (x) the derivative to find is, dydx = dydtdxdt

Q: I. Find dy/dx of the following: 1. y= In 2x 2. y (In x) 3. y= In(tan x)

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Show that L{cos at} = S s² + a² Hence find L{sin 8t sin 6t}.

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Q: dy 11. = cos(In z) dx

A: The given data is: dydx=coslnx  To solve the differential equation.

Q: If y = In(x² + 5) + sinx function then ay at x = 0 is ? dx 11 10 1 10 O 1 O 5

A: Given, y=lnx2+5+sinx  We have to find  dydx at  x =0

Q: To evaluate 3cosx -1 1- sin?x dx, the integrand can be transformed to A J(3 cos x - sec²x) dx ® S(3…

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Q: 21. If y=(x* +sin x)", then dy dx (A) 6(x*+sinx) (4x-cos.x) (B) 6(x*+sinx) (4x' +cosx) (C)…

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Q: 1)Find dy/dx for following functions. 1) y = (In 4)* + In () (Inx)2+ (In Vx)3 3* 2) y = tan-1 (x*)

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Q: (a) Show that cos(x²) > cos x for 0 ;. 1

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Q: dy Find for y=7x sin x+14x cos x-14 sln x. dy

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Q: I. Find dy/dx in the following: 3. Y= tan (1+sinx)

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Q: Find dy/dx for the following : 9) y* = sin-1 x %3D 10) y = xtanx + sin-ly 11) (Vy)* = (In…

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Q: (d) lim In(cos r) エ→0

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Q: Compute for the arcsinx dx . Which of the following is not an antiderivative of the function f(0) =…

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Q: Find dy/dx for the following: 6. (sinvx csc Vx) 9) y* = sin-1 x 8) у%3D 10) y = xtanx + sin-ly 11)…

A: Solution: Hey, since there are multiple questions posted, we will answer first question. If you want…

Q: Find dy Ldx For the following (Jy)' =(In tan x)(x") ( sin x)"

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Q: I. Find dy/dx of the following: 1. y= In 2x 2. y= (In.x) 3. y = In(tan.x)

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Q: 1 cos 3x dr b) VAr + 7 (In z)3 dr xe²? dx d) ſ e™ sin(e") dx e) f) sin x tan x dx (Hint: tan x = cos…

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Q: 1.) Evaluate In 2 e*2arctan e* J (1+ e2x) sec(2arctan e*)' А.) -dx. ežr(1 – e*r)- (arcsin e 2x) cos²…

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

Q: Show that where n is a positive integer.

A: To show

Q: What happens if you can write a function as a composite in differentways? Do you get the same…

A: 39. Part a). It is given that, y=cos u and u=6x+2 Therefore, dydu=-sin u  and  dudx=6 So,…

Q: dy Find if y = ln x5 + e-cos 2x – In e?. dx dy 5 ,cos?x-sin2 x dy 5 4 sinx cos x = - dx e sin2x-cos2…

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Q: 1)Find dy/dx for following functions. 1) y = (In 4)* + In ( 1 + (Inx)2 + (In vx) 3 3x 2) y = tan-1…

A: Use formula of derivative  to solve

Q: 1. Find for the following functions : dx 4i) y-bmcx* +2y}kos x (ans.: 4x.cos x - 2 In( x² + 2 )sin x…

A: To find the dy/dx of  y=[ln(x²+2)²]cosx

Q: Find dy/dx for the following : 7) y = 3ln (sec2x) eln(cos-1x²) sin/x 8) y = csc Vx 9) y* = sin-1 x…

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Q: - arctan(e**) dx =? 1+e2kx A) (arctan(e*)In [cos(arctan(e*)| + S In [cos(arctan(e*)da]+ c kekz B)…

A: Let I=∫tan-1ekx1+e2kxdx where tan-1ekx=arctanekx Put tan-1ekx=t…

Q: dy Find dx if y = a (sin (1))". dy

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Q: Compute Cos (x + k ) cos a dx by using substitution technique where k is a constant. [Hint: cos(A±…

A: The given integral is cos(x+k)/cosx.

Q: Н. W.4 Find dy/dx for the following : 7) y = 3ln (sec2x) eln(cos-1x²) sinx csc x) 9) y* = sin-1 x 1)…

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Q: Find dy/dx if y = In (tan(x). 3sec(x) + /sin (x³)

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Q: find (In x)³ dx 2x In (In x) dx x In x 11. 12. In9 et/2 dx tan x In (cos x) dx 13. 14. In4 eVi cdr…

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Q: Find the antiderivative of 5$sinx ln 5 cos x dx. A.) 5cosx + C B.) 5sinx + C C.) 5sinx In 5 + C 5sin…

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Q: 1) Find dy/dx if : y In (tan¬ x)

A: Given : y = lntan-1x

Q: Find dy/dx for the following : 1) y = x + sin x² + stn-! 5x 2) y = 32x + In (stn x²) + In(sin-1 5x)…

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Q: Sind dy/dx if cscax oftxth)= Sin a(x4h) sinax + sina(xth) E sinaxcoçaht cosaxsinah

A: given,

Q: I. Find dy/dx in the following: 1. Y= sin In(x + 1)

A: To find the derivative of given function.

Q: dy.xandy in =cos = COS e

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Q: dw Find dx where w = cosz- cos 4x cos'4y + sin 4x sin 4y and z= 4x+ 4y. dw 口

A: lfirst put value of z and then expand cos term Now we get Zero whose derivative is zero

Q: Q1 Evaluate the following: Ine dx n/3 4 sinx 1- Jo 2- Jo x(Inx)2 3-m 2e*cose*dx in 1-4cosx

A: Simple integration problem.....