Find f'x) usig the denivative rules, f (x) = 2 Sinx - COSX + tan X

Q: IT Evaluate the integral: (cos x + sinx cosx)dx

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Q: If x = ln ( sec x + tan x) , show that sec x = cosh x

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Q: Differentiate the function. f(x)  = In (Sin2x)

A: Use chain rule

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of • sin ( x ) h(#) = | , -…

A:

Q: : Prove thati Od tanx= sec>x 2. 3d secx= sec x tan x 2: find first derivative following Bi funCtion…

A: Prove that1. d(tan x)dx=sec2x2. d(cot x)dx=-csc2x3. d(sec x)dx=secx·tanx4. d(csc x)dx=-cotx·cscxSome…

Q: Find the derivative f'(x): f(x)=x4-x2+sin-1x/3 **4-x2 is under a radical sign!

A: Consider the given function f (x) taking (4-x^2) under the radical sign. Differentiate f (x) w.r.t x…

Q: Solve the derivative: sinx – 1 F(x) = COSX Answer: sec(x)tan(x)(sin(x) – 1) -

A: We will find the derivative.

Q: 1/tanx+secx=cosx/sinx+1  verify

A: We simplify the left-hand side first. Multiplying by (secx-tanx) in numerator and denominator.

Q: 7/3 x tan (x) dx 2

A:

Q: Verify that the derivative of sec x is sec x tan x. (Hint: Use thefact that sec x = 1/cos x.)

A: To Determine: Verify that the derivative of sec x is sec x tan x.  Given: use secx=1cosx…

Q: 6) f(x) sin x %3D tan x %3D

A: We can find the derivative as below.

Q: compute the derivative.  f (x) = (cos2 x)cos x

A: To compute the derivative.  f (x) = (cos2 x)cos x

Q: Verify the derivative of cosine (use the definition of derivative). d[cos(x)]=- sin(x) dx

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Q: Find tanget line to f(X) =tan(X) + 9 cos( X) at X=π

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Q: Consider the function f(x) whose second derivative is f"(x) = 9x + 5 sin(x). If f(0) = 3 and f'(0) =…

A: The function f(x) whose second derivative f''(x)=9x+5 sin(x)f(0)=3 and f'(0)=2

Q: Let f(x) = cos(arcsin(x)). %3D a) First find the derivative by using Chain Rule f'(x) =||

A: (a) Given function is : fx=cossin-1x Now differentiating given function with respect to x using…

Q: 16. Using the Quotient tanx= sinx/cosx to prove d/dx tanx=sec2x

A: Quotient rule of differentiation

Q: Use the quotient rule to differntiate the the function. f(x) = [ tan x-1/sec x]

A: Given: fx=tanx-1secx we know that ddxuv=vdudx-udvdxv2                                          ..1

Q: 9. Determine f'(x) where f(x)=tan sin(7x).

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Q: Differentiate f(x) = sinh (x) + 2 cosh (x) - sech (x)

A: Aim: We have to differentiate given function.

Q: What is f (=) if f (x) = sin 2x + cos 2x + sec 2x + 8 %3D csc 2x + tan 2x + cot 2x.

A: The given function is fx=sin2x+cos2x +sec2x+csc2x+tan2x+cot2x. To find : the value of function at…

Q: Compute the derivative.   f(x) = sinx cosx

A: f(x)= sinx cos xf'(x)= ddx(sinx cosx)        =sinx ddxcosx + cosx ddxsinx        =sinx (-sinx) +…

Q: f(x)=rad(3-sinx/4-cosx)

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Q: Let f (x) = sin-1(cosvx). Find f'(x).

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Q: tan2 (3 + Ax) – tan2 3 lim Ar 0 Ax

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Q: 1 Differentiate f(æ) = sin-(4x). Use exact values. = (x),f

A: We use the chain rule for differentiation

Q: What is the derivative of f(x) g(x) in terms of f and g? Compute the derivative of -sin(x) · 2x=1…

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

Q: Using suitable method, show that 2 tan" (x+2) dx =- – In 2 .

A: We use integration by parts to find integral tan inverse x.

Q: (a) Show that tan x = dx sec?x using quotient rule.

A:

Q: Show how to extend the functions to becontinuous at the origin. ƒ(x) =tan (tan x)/sin (sin x)

A: It is given that fx=tantanxsinsinx

Q: Find the equation of the tangent line to the astroid x = cos° (0), y = sin³ (0) at 0 = 5. (Express…

A: The given equation of the astroid:x=cos3θ and y=sin3θWe need to find the tangent line to the astroid…

Q: Differentiate f(x) = sin-(2x). Use exact values. f'(x) =

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Q: 2 cot x-3 sin²x sin x

A: NOTE: Refresh your page if you can't see any equations. .

Q: Use cos(sin^(-1)x)=Sqrt(1-x^2) to determine the derivative (sin^(-1)x)'

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Q: 16. r(0) = sec 0 tan 0 – 2eº -

A:

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of sin(x) (cos(t²) + t)dt…

A: Given that , hx=∫-1sinxcost2+tdt h'x=?

Q: f(x) = ln(125 sin^2(x))

A:

Q: The derivative of sec² 2x (cos² r - sin² x) with respect to a is O2 sec 2x tan 2x O4 sec² 2x cot 2x…

A: Find the derivative

Q: If f(x) =>(1- (sinx)²)" .Determine the value of f)

A: use the trigonometric identities to simplify and the solve. detailed explanation is in step 2 answer…

Q: Differentiate the function. f(x) = sin(x) In(3x) sin (x) f '(x) + cos (x) In (3x)

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Q: In(cos(x)) Find the derivative of cos(In(x))

A: Derivative using quotient rule (f/g)'=(gf'-fg')/g2

Q: If f(x) = sinx + cosx sinx - cosx 2 show that f'(x) = sin 2x – 1

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Q: 6: By use of the product rule, differentiate the function f (x) = (x² + 1) sin(2x).

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Q: The first derivative of the function tan2x sec2x C) sec2x cos2x O A) 2sin(2x) O B) (1-cos4x) O

A: It is known that ddxsinbx=bcosbx, where b is a constant.

Q: Find f"(x), where f(x) = tan-(sin x2019)

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Q: Show that F(x) = tan2 x and G(x) = sec2 x have the same derivative.What can you conclude about the…

A: Given:Fx=tanx2Gx=sec2x

Q: 3-sinx 6. f(x) = 1+ In(x3 — х)

A: Quotient rule of differentiation: Chain rule:   also

Q: d. tion to prove that (cscx) dx = – CSC X COt x. 86. Use the quotient rule and the derivatives of…

A:

Q: f(x) = In(sin² x)

A: Given,           fx=lnsin2x

Q: Find the domain of the second derivative of the equation (image)

A: Given:

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.