Question:4 Calculate by implicit derivatives (tan x)" + ycotx + sinxy – exy – In2 = 0 - dx

Q: Find the first derivative: y = 3 arcsin(cos 2x) %3D O-7 O -8 O -4 O-6 O-5

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Q: 1 S cos³ 3x sin' 3x dx

A: The given integral is: I=∫cos33xsin43xdx   ...1   We know that; The Power rule: ∫xndx=xn+1n+1+C

Q: VT (2x)[sin (2x²)] cos (x²) your exact-value result. Evaluate dx. Show complete pencil-and-paper…

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Q: 12. y = −3 cos (0 + 1) − 2 Amplitude: Period: Phase Shift: Midline:

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Q: 2. ( sin32x dx cos 2x

A: We have to integrate.

Q: 6. Find Sin 5x (b) y = THcos 5x dx

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Q: 4. S sin(tan-1 t) -dt 1+t2

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Q: dx sinh x - cosh x

A: To Evaluate: ∫dxsinhx-coshx Concept: i. ∫afxdx=a∫fxdxii. ∫exdx=ex+C

Q: Question D. Use implicit differentiation to find all the derivatives. 1 3yz? - cos 4z – 3y² = 4 xyz…

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Q: S sin 2x sin 4x dx 7.

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Q: f(x)%3D-2 sinx+2 Amplitude D %3D Equation of mid-line: Length of period: Phase Shift:

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Q: C. y = cosh¯'(x² + 1) + tanh-1(sinx) + sinh-'(cothx²)

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Q: |(sin 3x + cos 2.x)* dx

A: Given integral is ∫sin3x+cos2x2dx

Q: 3. S sin*2x cos$2x dx

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: y= sin(x + 4) cos (x - 4) y= sec 4x + tan 4x y= Arctan

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

Q: 1-sin(x) (1-Sinx)2 10. Find the equation of the line tangent to the graph of y = 3cos(x) at the…

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Q: Cos 2x dx ) Sin*2× + 8 1.

A: Given ∫cos2xsin22x+8dx

Q: (#6) S sin³ (x)dx =

A: Given  Rewrite  sin3x=  sin2x * sinx  Use Pythagorean identity sin2x + cos2x=1

Q: S sin5x cos³x dx

A: Given∫sin5xcos3xdx

Q: a) y = In x · sinh x*

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Q: 1. cos x sin“ x dx

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Q: 1. 8e* sin(4x)dx TC

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Q: 2. Find the derivatives of the folowing equations: y = sin-'(1 -t) y = csc-(x/2) y = In(tan- x)

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: dx 6. [- xIn x sin 5tdt 7. V1+ cos 5t

A: Given that the integral ∫dxxln2x. Give suitable substitution to simplify the integral. Let u=lnx,…

Q: | cos²x dx 1- sinx cos-x

A: Given. f(x) = cos2 x/(1-sinx) We need to calculate the indefinite integration of above function

Q: 11. y = 2 sin(0) + 2 Amplitude: Period: Phase Shift: Midline: 2n 3x H 4 ST

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Q: S sin-1 3x dx

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Q: 2. Integrate | sin x cos? x dx

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Q: Cos 4x S cos 2x-sin 2x dx

A: This is a problem related to integration. Based on the general formula and concepts we will answer…

Q: -dx 1 – sin(0)

A: To evaluate the integral.

Q: A. sin(3x) dx

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Q: 3 sin x 1. S- dx 1+cosx

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Q: Si cos°(3x)sin (3x) – cos (3x) sin°(3x) dx

A: First we common out cos7(3x) sin7(3x) and then apply the formula cos2(3x)-sin2(3x)=cos(6x)

Q: S sin(4 + 5x) cos (5x – 4)dx

A: From the given problem: I=∫sin4+5xcos5x-4dx As we know that the trigonometric identity:…

Q: sin 3x dr + 2y cos* 3x dy = 0 COS

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Q: dy -1 Find when x = 0, if given y = tan (sinh x). dx

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Q: ope of the curve 2xy = In(e*) sin(x)

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Q: 4. sin 2x cos 2x dx

A: Here we integrate the given function.

Q: 16. S sin 3x cos 3x(cos 3x+1)² dx

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Q: 4. cos 4x cos 2x dx

A: The integration of the integral is cos(4x)cos(2x).

Q: evaluate the integral.

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Q: the slope of the tangent. line to: the graph of y=XT COSXY the point (0,1)? What is of: 4=XT COSメ

A: Given: y=x+cosxy

Q: 50 6x sin dx e sec sec

A: The question seems to be wrong. I have made a few changes. The solution is as follows below:

Q: 3e" - 2 sec x tan x + cos x - 3 dx 1+x?

A: Given:

Q: cos x -dx Compute the integral 1+(sin x)²

A: replace sinx=u cosxdx=du limits of u will be 0 to 1

Q: b- S sin5x.cos²x.dx

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Q: 1. cos x sin* x dx

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Q: evaluate the integral.

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Q: S sin(3x)cos(2x)dx

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Q: 5x cos dx 2 x3 cos 9x dx X' COS

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: