9. [sin Ssin' cos–dx 3 3

Q: find dy / dx by implicit differentiation.

A: In implicit differentiation, on differentiating y, we use dy/dx.

Q: Evaluate sin (44º) + cos (29º) using differentials. Refer to special triangles.

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Q: (24) Evaluate the integral: | Va sin(1 + x/2)dx.

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Q: Evaluate ]e * cos (7x) dx. Seex cos (7x) dx = %3D

A: Explanation of the answer is as follows

Q: What is dy/dx of 1/2e^2x

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Q: (2y-1 + cos 3z) 분. 4x3 + 3y sin 3x = 0 (1)

A: We know that if - M(dy/dx)+N=0 Then M(dy/dx)= -N Therefore- dy/dx= -(N/M)

Q: Compute d/dx  sin-1 (x/x+1)

A:

Q: 4. Evaluate sin (44°) + COS (290) using differentials. Refer to special triangles.

A: To evaluate  sin440+cos290 using differentials.

Q: nasin(hx) cos(bx)dx

A:

Q: (4) 3. Use implicit differentiation to find dy/dx of the following: x² - 5xy + y³ = 21

A: As per policy only first question is answered. Please refer to the image below

Q: Let 5 sin æ + 6 cos y = 6. dy dx d?y dx?

A: 5 sinx +6 cosy = 6  Differentiating w.r.t x,  5 cosx +6 (-siny) dy/dx = 0  dy/dx = 5cosx/(6siny)

Q: dy by implicit differentiation if dx 3 9. = 1. Find - -

A: The given function is 3y+9x=1

Q: Find integral.

A: We have to find the integral I=∫cos(5x) dx

Q: x sin 2x sin cos x 2 Prove that: dx = 2x- T

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Q: S" sin" (0.5x)cos (0.5x)dx

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Q: 10. Find , if y = dy 1-cosx dx 1+cosx

A: Given  y = (1- cosx) /(1 +cosx) To find dy/dx

Q: Which of these is the differential of y = x· cos x ?

A: From the given data:

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

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

Q: cos (In z) sin (In x) dx

A: To Evaluate the integral

Q: Integrate: | cos" z dx

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Q: If we have to check the DE sin(x). dy +y cos(x) = 1 dx for Exact then My = - sin(x) -sin(x) -cos(x)…

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Q: d Verify tanh - = X 1- x2 dx

A: Inverse hyperbolic tangent function can be expressed in logarithm funtion. Write tanh-1x=12ln1+x1-x…

Q: 3. S sin x In(cos x) dx

A: According to company rule, we can answer only first question.

Q: 1od of undc cients, obtain the general y" – 2y' – 3y = 2 sinx

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Q: (b) Show that 2t cos x and sin x = 1 + ? (c) Show that dt dx 1 +

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Q: f'(t) = sin 8t - cos -/-

A: You are correct

Q: -6e' sin(at – 3) dt

A:

Q: 1. Calculate the Integral sin x cos x dx

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

Q: find dy / dx for Hhe tellowing in (sec EX) In (cosp?}

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Q: 10. J(3x3 — 5х + sin3x) dx -

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Q: S sin(3x + 2) cos(1 – 4x)dx

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Q: 1. S(esin x cos x - acos 2x sin 2x)dx

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

Q: roo sin(2) Compute (4) dx. fo x(x²+4)

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Q: 33. Prove for a > 0: dx x2 + a 1 tan Ja

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Q: Use Property 8 to estimate the value of the integral.

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Q: f(x) = cos (In (3x))

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Q: 4. sinh(z²) dz dy dx

A: We need to solve the triple integration by re arranging the order.

Q: 4. Ify =/sin x+ /sin x+.to inf inity, dy _ cosx dx 2y-1 prove that

A: Derivative of Sinx is Cosx

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: 1) If f(x)= tan(5x), find  f'(5)=??????

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: 7 Find (b) x siny-ycosx-y 1.

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Q: 7. Integral cos x dx sin x

A: This question is related to integration, we will solve it using given information.

Q: 2n Sin (3y) dx + 3x Cos(ay) dly =o

A: Given differential equation is 2xsin(3y)dx+3x2cos(3y)dy=0

Q: Find at the point (1,0) for cos xy + ye* = 0. dx

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Q: 4. Evaluate sin (44°) + + COS (29°) using differentials. Refer to special triangles.

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Q: 2T COs x dx

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Q: Evaluate sin integral (4x) cos(5x) dx

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Q: Show that ∫∞−∞ sin x dx diverges.

A: To Show: ∫-∞∞sinxdx diverges.

Q: find dy / dx for Hhe follo wing 2X y=3+ ln (sin x?)+In (sin 5x)

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Q: Show that Sx cos*x dx = (x² + x sin 2x +cos 2x) + c

A: Given: ∫xcos2x dx=14x2+xsin2x+12cos2x+C.