DI Ify x Sin x, x'sin x, .2 O a) 2 sin +x cos x O b) 2x sin x + x I SOƆ cos x O) 2x sinx - x cos x Od) 2x + COs x Oe12.sin(1) +66 cer

Q: secx tan.x 5) 1+ sec x

A: Use the method for substitution.

Q: 18) e2x = sin(x + 3y)

A:

Q: -5 sinx dx I = =? ecosx +3e-cosx ) +c COSX a) arctan 3 cosx b) arctan + C

A: To find ∫-5sinxecosx+3e-cosxdx

Q: Let y = cos(sin(90)). Then y" is equal to: Q8 -81 cos (90) cos(cos(90)) + 81 sin(90) sin(cos(90))…

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

Q: 11) fx-In x dx In x- 2 4 (ans. : -+c) 12) fx- tan'x dx (ans. : 2 -tan"l x -(x- tan"" x)+c) 2 13) fx'…

A: 11.Given,∫x.In x dx

Q: 1. Explain why sin(n+0) =-sin@ using a diagram and x, y, and r.

A: Solution of given problem is followed by

Q: Lan: prove (:) - - 4. sin x tan =1- cos x

A:

Q: If cos x = sin 2x cos 2x tan 2x = 4 5 csc x<0, then " ;

A:

Q: Let f(x)=sinx.When x=and dx=,then dy=? a) √2 b) cosxdx π+2 c) sin (+²) - sin() d) √2 √2 con()+sin()…

A:

Q: b) sin 3x 3 sin x – 4sin3 x [Hint: sin 3x sin(2x + x)] Prove

A:

Q: 13) 3 sin x +5 sec x tan x cos x dx

A:

Q: B) prove du d 1. sec u = secu tan u %3D dx dx

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Differentiate a $sin "(z) with respect to sin x.

A: We will find out the required value.

Q: appropriate formula for 9. What is the f sin7 x cos x dx ? A) sin x cos x dx | cscx cosx dx B) C)…

A: We have to find solution of given indefinite integral.

Q: tan y-1 . sin y- cos y- 1 www. Prove that tan y +1 sin y + cos y+1 2.

A:

Q: そ COS X d x Sin X

A:

Q: Differentiate. ' a) y = 2cos(x²)

A: Hi, at a time we can answer only one question and the exact one was not specified. So, I have…

Q: Q3) A: Find y if: a- y = sin 2x + 2 cos x c- y = sin √x (As... b- y = secx. csc x d- y = tan(2x + 1)

A: Please see the attachment

Q: 3) 3 sin x + 5 sec x tan x COS X dx

A:

Q: 2. Prove the following identities. = tan (x+2) 1tanr 1-tanx b) sin(π-x) - tan(-x) = sin2x c) secx =…

A: By the answering guidelines of Bartleby, We can answer only first three subparts, please post other…

Q: b) L{e" sin(3t)}

A: b) We need to evaluate the Laplace transform of the following expression e2tsin3t

Q: i) etan-¹x 12 1 + x² dx ii) ii) sin sin5 x dx

A: Solve the following

Q: Find where w= cos z - cos x cos 2y + sin x sin 2y and z x+2y. Me.

A:

Q: 4. lim 3 sin (tan¹x)

A:

Q: 2. Show that cot x cos* x +C 4 cscx csc x | cot? x csc*x dx = - 6. 4 6.

A:

Q: 4/ Prove that: " cos bx dx = (bsinbx +a cos bx]+c

A: