cos (x + h) – cos x f'(x) = lim h0 57. h cos x cos h – sin x sin h – cos x lim h sin h cos h = lim ( (- sin x) h→0 + (cos x). h h = (– sin x) · 1 + (cos x) · 0 = – sin x

Q: 2+tanx If f(x) = find f'(x) 2-tanx

A:

Q: Find g'(x) if g (x) = 5√x tan x. 5(2 cot x+tan x) 2√x 5 tan x(2x sec x+1) 2√x 5(x sec² x+2 tan x)…

A:

Q: 2. Use the definition = f'(x) = lim f(w)-f(x) to find the derivative of y = tan x. dx w-x

A: Let's take; w - x = h w = x + h As w approaches x; w-x = h →0   f'(x) = limh→0  [f(x+h) - f(x)]/(h)…

Q: Let f'(x)= = f(x) = x² tan ¹(7x)

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Q: Let Find f(x)\x= = ". y = f(x) = 31 sec x + 18 tan x 31 sec x 18 tan x d dx -f(x)\ x= 1 *

A:

Q: 2x2 tan z If f(x) = find sec z f (x) = Find f (5)=

A:

Q: If f(x) = = sin (3 – x), then f'(0) O 6 sin 3 cos 3 O 6 cos 3 O -2 sin 3 cos 3 O -2 cos 3 -2 cos O 2…

A: f(x)=sin2(3-x)

Q: x sin if x # 0 Show that the function f(x)= is differentiable at x = 3D0 and f '(0)= 0. if x = 0

A: A  function is  differentiable at  point c if L f'c=R f'cwhere L f'c=limx→c-fx-fcx-c   =left hand…

Q: f(x) = -2x cos(x)

A:

Q: Q2/ Find f (x) : 1- f(x) = 4 cos x + 2 sin x 2- f(x) = cos x - x csc x 3- f(x) %3D %3D cot x 1+cscx…

A: As per guidelines we can solve only one question at a time. So the first question can be solved as…

Q: Find f' (x), if f(x) = sin(2x* – sin(x))

A:

Q: tan x – 2 f(x) sec x find f' (x). (1+2tan(x))/sec(x) Find f'(). (1+2tan(pi/6))/sec(pi/6)

A: To solve the derivative of the following function.

Q: Let f'(x) = f'( 5 ) = f(x) = 3 sin x + 12 cos x

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Q: If f(x) = f'(x) = ƒ'(1) = = 2 sin x 3 + cos x > 3 cos (1) () then 3 cos (x) + sin(x) (3 + cos x)² X…

A:

Q: 3 a Differentiate b Differentiate sin x and hence find an anti-derivative of COS X cos(2x) sin(2x) 1…

A:

Q: Let f(x) (8 sin x + 3 cos æ)tan-x f'(x) =

A:

Q: Let f(x) = (7 sin x + 2 cos x)tan-lx f'(x) = %3D

A: topic - derivatives

Q: If f(x) f'(x) = COS x 3 tan x, then - f' (5) =

A: Derivative of cosx is -sinx.

Q: LIf f(x) = 2 sin(x) + 2x* , find f' (3). f'(3) =

A:

Q: The definition of the derivative of a function is f'(x) = lim f(x + h) – f(x) h→0 h Write, but do…

A: Given: The definition of the derivative of a function is f'x=limh→0fx+h−fxh I. fx=2xsinx II.…

Q: 4 tan(x) Let f(x) -. Find the following: 4x sec2 (x) – 4 tan(x) 1. f'(x)= %3D 2 2. f'(1)= %3D

A: We know quotient rule for differentiation is  ddxfxgx=gxdfxdx-fxdgxdxgx2

Q: f(x) = 7 sinx+ 5 cos x

A:

Q: The derivative of the function f (x) = 3 sin“ x is Select one: O f'(x) = 12 cos³x O f'(x) = 12 sin³…

A: dsinxdx = cosx

Q: If f(x) = cos(x), what is f'(x) ? O -sin(x) O cos(x) O -cos(x) O sin(x)

A:

Q: Find f. F"(8) = sin(8) + cos(8), f(0) = 5, = 5, f'(0) f'(0) = 3

A:

Q: f'(x) = f(x) = cos(2x + 3)

A: Given query is to find the derivative.