7 sin x Let f(x) 6 sin x + 2 cos x Then f'(x) = The equation of the tangent line to y = f(x) at a = 3 can be written in the form y = mx + b where т — and b =

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A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

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Q: Differentiate the following. (a) y = sin(x3) (b) y = sin3(x)

A: For (a), y'=sin x3'     By the chain rule,   =cosx3x3'     =cosx3· 3x2

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A: Here we use use substitution method to evaluate the given integral.

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A: First, we simplify the given function using the multiplication and power rule of logarithm.

Q: #51

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A: Differentiate above equation with respect to x.

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A: We have given equation  y=x13+cosx Put x=0  y=0+cos(0)=1 Point on the curve x1,y1=0,1…

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Q: 3 cos(x) sin(4x) 3. lim x→0 2x

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A: To find the following parts,

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Q: The third derivative of y = sin is 1 -sin b) y" = --cos 1 а) у 8. 2 2 c) y" =-8sin d) y" = -8 cos

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Q: 4. The 1" derivative of y : cotx a) xsec?x + tanx b) xsecx - tanx c) cot x + xcsc'x d) cot x - xcscx

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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: elin (sin x+ cos x) dx 1. S ecosx

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

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Q: 6) By implicit differentiation find a) xy + y² = 2 find d²y/ dx² %3D b) sin(x²y²)= x find dy/dx

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Q: 2. f(-7sinx + 3cosx)dx (-7sin 3. √(3x − 2 + sin x) dx TE 4. (3 sec² x + 4 csc² x) dx

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Q: 12. Find the first derivative of y = 2cos(2 + x*). A. -4x sin (2 + x2) B. 4x cos (2 + x*) C. x sin…

A: Questiopn no. 12,Given,           y=2cos2+x2To find : The first derivative of the function.

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A: Given differential equation is y'''−y''=3+sinx. We have to find the general solution of the given…

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A: Given:-(a) y=sin(x3)(b)y=sin3xwe have to differentiate(a) y=sin(x3)differentiate with respect to…

Q: )Find the anti derivative for sin(x^2) 2x

A: we have to find the anti derivative of ∫sinx22xdx...............1 first we put in place of x2 =z…

Q: ind the equation of the line that is tangent to y = 2x + sin x + cos x at x = 0.

A: NOTE: Refresh your page if you can't see any equations. . take x=0 the point on the graph is

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A: Let y= (1+sin2x)^(1/x)Then take ln on both sides.

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A: Using the formula of cos(A-B)=cosAcosB+sinAsinB. Explanation is given below..

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

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Q: Find the x-coordinate of all points on the curve y = sin(2x) + 2 sin(x) at which the tangent line is…

A: Determine the derivative for y. y=sin2x+2sinxy'=ddxsin2x+2sinxy'=ddxsin2x+ddx2sinxy'=2cos2x+2cosx

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Q: ∫(3 cos(x) − 7sinx(x))dx   Evaluate indefinite anti-differentiation

A: