Differentiate: y = 5 tan? (25x) O y' = 750a? tan(25a³) sec2 (25a) O y' = 7502 tan? (25a) sec(25a*) O y' = -750z? tan (25a) sec? (25a*) | y' = -7502? tan² (25a³) sec (25x)

Q: (5x) S sin(x) tan(x) .........

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Q: 4) Estimate tan (0.5) using the tangent line to y = tan(x) %3D 6

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Q: Integrate sin^2(7x)-cos(x)

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Q: SOLVE USING VAREATION Of PARAMETERS OR REDUCTION of ORDER 2 tan'x

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Q: determine the general derivatives f(x)= -3 f(x)= sin x + cos x -sec2x

A: Simple use the identity of derivative of constant is zero and derivative of sinx is cosx and…

Q: Find the derivatives of the functions y = 2 tan2 x - sec2 x

A: Given  The function  is y = 2 tan2 x - sec2 x Formula

Q: Find the equation of the line tangent to the graph of f(x) = – = -3 cos (x) at x = 3 m(x – xo). You…

A: given: the function f(x)=-3cos(x) the point is x=-π3

Q: sec?x Integral tanx

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Q: 1. Find the derivative of f(x) = tan³(sinx) + %3D

A: The given function isf(x)=tan3(sinx)+x3+3x4

Q: Find the derivative of y with respect to x. 2x + 3 26) y = sec = sec-1 27) y = -sin-1 (5x2 + 2) 28)…

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Q: Differentiate : a. y= x^2 sinx +sin^2x + cos^2x + tan 2x/sin2x/cos2x b. y= In √x^3

A: a) y=x2sinx+sin2x+cos2x+tan2xsin2xcos2xb) y=lnx3

Q: Find the function who’s derivative is dy/dx = tan(x)sec(x) - 9x^2

A: Given: dydx=tanxsecx-9x2   As we know that; The Power Rule: ∫xndx=xn+1n+1+C And the common integral.…

Q: Find the coordinates of the point on the graph of y = 8 sin x+4 cos (2x) + 14, 0 <x<5, where the…

A: Consider the given function, y=8sinx+4cos2x+14 The slope of the tangent line on the given curve will…

Q: The derivative of sec2 2x(cos2x−sin2x) with respect to x is

A: Given: f(x)=sec2 2x(cos2x−sin2x)   Simplify the function before finding the derivative: By  the…

Q: The first derivative of y=cos(tan(x2-7x+1)) is.. 1. O -[sin(tan(x²-7x+1))][sec²(2x-7)] 2. O…

A: Find the derivative of y=costanx2-7x+1

Q: Solve for the derivative of y=sec3(2-3x) With the answer 9 sec3(2-3x)tan tan (2-3x)  Show…

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Q: Find an equation of the tangent line to y sin 2x = x cos 2y at the point π/2 , π/4 . Do not…

A: First we will find Differentiation of given equation to get slope of the tangent line. Now equation…

Q: What is the derivative of cosh-1(xy) + elog x = sec3(y2)

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Q: Look at the graph of y = tanx. For y = tanx, as x --> π-/2, y --> ? For y = tanx, as x --> π+/2, y…

A: Given

Q: f6)= Sin () (x 3x26x-8) 1 CosX In Ceos x) | $66)=Sinx+t Cosx. sinsetl -6()=DSin -2053 2.

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

A: Aim: We have to differentiate given function.

Q: Apply the first derivative test to indentify all relative extrema. f(x) = cos² (2x)

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Q: f y=sin(sinx) show that y'' +(tanx) y''+y cos2x=

A: Given that y=sinsinx To show that y''+tanxy'+ycos2x=0

Q: Find the derivative. y = sinh 1(tan x) O y = |cos x| O y = 1 /1+tan x O y = 1 Vtan? x-1 O y = |sec…

A: In this we have to find integration and derivative.

Q: Lim as x approaches 0  1-cos(5x)+sin(3x)/x

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Q: Evaluate / 5 sec2 *dx tan(x) 05 In(|tan(x)|) + C Oln(tanx) + C 05 In(x) + C 05 tan(x) + C

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Q: tan2 (3 + Ax) – tan2 3 lim Ar 0 Ax

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Q: Is it true that the derivative of y=arcsin(cos2x) is -2?

A: The function is y=arcsincos2x.   Differentiate the function with respect to x.…

Q: Find the 1st Derivative. r=( 2 tan3θ -1)1/3

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Q: Find the derivatives of the functions in Exercis

A: we have to find the derivative of the given function. g(t)=1+sin3t3-2t-1

Q: find the root of 3x +sinx -e ^x=0 using secant method

A: Let us consider the function fx=3x+sinx-ex. We have to use the secant method to find the…

Q: Find sine half range for f(x) = \cos x for -1<x<1 COSX for < x < 0. f(x) { COSX for 0 < x < .

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Q: The second derivative of y = ln(sec x) is а) у 1 - tan x b) y = tanx sec x c) y = secx · tan x d) y"…

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Q: 1) y = sin(1 – x²) 2) y = tan 'Vx² + 2x 3) y = tan1 Vt²-1 + csc 1t

A: Given the trigonometric function

Q: Find the derivative 1. h(x) = cos3(tan2x) 2. h(x) = x5 sec(1/x)

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Q: Differentiate with respect to x. Y=sin5x

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Q: The derivative of sec(e) is tanx O 1) tan(e*") sec{e*™) O 2) tan(e**) sec(e*)x e** 3) tan(e)…

A: topic - derivative of a function

Q: 2cosx dx 5- f 1+(sinx)2 a)2 tan sinx| b) 2 In sinx| c)2 In(1+ (sinx)1

A: We use Trigonometry substitution method

Q: What are the indeterminate forms and L'hospital's rule in application of derivatives?

A: We have to define Indeterminate form and L'Hospital Rule

Q: Evaluate: S 0 tan¬(0)d0 arctan(8)–0 Sarctan 0 + C 2 arctan(0) 0 zarctan 0 + C 2 arctan 0- 0…

A: Please refer the attached image for complete solution.

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: Find the linearization of ƒ(x) = sqrt(x + 1) + sin x at x = 0. How is it related to the individual…

A: To determine the linearization of the function at x=0.

Q: Choose the derivative of tan-(x). 1 x /x² – I 1 1 + x2 1 V1 – x² - 1 1+ x2 1 /1 – x² | 1

A: Sex2x=1+tan2x

Q: How did he get the second derivative step by step and a clear line please 3 F(x) = 1+e siny x Fex)…

A: Let fx=1+e-xsin 4x

Q: Compute the derivative d tan x dx \cos x COS X 4 sec2 x – sinx tan x 1– 4 cos x + tan? x - | (cos x…

A: We have to compute the derivative of the given function: ddxtan xcos x-4 We know the formula of…

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 sine half range for f(x) = \cos x for -t< a <n %3D cosx for f(x) for 0<x <n. cosx

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Q: Find a root of  x- sin(x) - (1/2)= 0 correct to four decimal places by Secant Method

A: The given function is: x-sinx-12=0 Let, fx=x-sinx-12 Here, f0=-0.5f1=-0.3415f2=0.5907

Q: find integral tan 6 x sec  4 x dx

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