3. Given f(x) = cot(x) sin(x) and g(x) = cos³(-x)(sec² (x)-1) sin² (x) a. Prove that f(x) = g(x). Show all steps that lead you to this fact.

Q: 6. Find the tangent line to the function f(x) = 2x cos"(x) (0, 1).

A: To find the slope we need…

Q: If find f'(x). Answer: f(x) = 4 sin x 3 + cos x

A:

Q: Find F(t) such that F'(t) = sec³ (t) tan³ (t) and F (3) = 0.

A:

Q: sin(x)ecos dx COS X 8.

A: Given,

Q: (В) f (x) 3 3 sin(2x) — 4

A: we have to draw the curve of the function fx=3sin2x-4 let y=f(x). therefore, y=fxy=3sin2x-4 the…

Q: Determine the lowest positive real root of f(x) = 8 (Sin x) (e-*)–1 using the Secant method. Take…

A: Solution: Given that

Q: tan¬'(t)+2t² t > 0 t f(t) = t = 0 a ,btan-'(t) t < 0 Find any real number for both a, and b, that…

A: Consider the given function, ft=tan-1t+2t2t   t&gt;0a                     t=0ebtan-1t…

Q: f(x) = 10 sin x + 9 cos x f'(x) = %3D %D

A:

Q: Consider a function f(x) where f" (x) = 5ª (ln 5)² + sin(- a) Find f"(x) dæ. b) Assume that f(0) = 9…

A: with the help of integration  properties we will evaluate the above function detailed solution is…

Q: Q:Findthe domain of the following functions sin 'x (1) s''x (i) [x] 1 (ii)- | x | ,× cos 'x

A: In this question, we need to find the domain of the given functions.

Q: If f(x)- 3 cos 4x- - {).₁ 0 -3 -12 4 find f'

A:

Q: ilf find f'(x). Answer f(x) = 3 sin x 1 + cos a

A:

Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: Find L {f(t)} if f(t) = cos 5t + sin 2t

A:

Q: Find approximate value of the derivative for f(wo)-6f(x1)+3f(x2)+2f(x3) fr(x2) = f(x) = 10 sin(20æ?)…

A: Introduction: Numerical differentiation is the technique of obtaining the numerical value of a…

Q: Dhcx)=cos (x+)

A:

Q: π/4 IF ST/A tan (x) sec(x) dx = I, express the value of 。 π/4 tan (x) sec(x) dx in terms of I.

A: Given:- ∫0π4tan4xsecxdx=I

Q: -1 Let f(x) = (3 sin z + 4 cos z)tan f'(x) = %3D

A: Given  f(x)=(3sinx+4cosx)tan-1xTo find f'(x):

Q: 7. Find the second derivative given g(x) = sin x² A. 2 (cos x² - x sin x²) C. 2x cos x² 9 "(x) - 4 x…

A:

Q: 27: let f(x) = tan(x)+ sec(x) find f"(x)

A: As per our guidelines, we are allowed to answer only one question. Since you have asked multiple…

Q: Consider the function f(x) = 4 sin(x) cos(x) + 6 csc(x). Evaluate its derivative at the point x =…

A: Product rule of derivative is used.

Q: 4. Prove that cos(sin¬1 x) = /1 – x².

A: cos(sin-1x)=1-x2⇒sin-1x=cos-1(1-x2)Let y=sin-1x                               (1) ⇒siny=x…

Q: Find the derivative of the following. a) y = cos (4x³ + x²-2) b) Y=xsin ''(x) + √√1-x²

A: