tan¹ (2x) x sin(3x4 + 8x³) f(x) = { [ / (x + ¹)] 1) cot-¹ cosh (³+-+1)). if x < 0 if 0 ≤ x ≤ 1 if r > 1

Q: Let f (x) = 6 sinh 1(tan(x) , O < x < 5. Find the slope of the line tangent to the graph of f at the…

A: Given: Here, we need to find the tangent line to the graph of f at the point on its graph where…

Q: : Q2) Find the derivatives of each of the following functions? 1- y= tan (V3x + In(5x)) 2 y In…

A:

Q: Use backward-difference formula to evaluate the first derivative of y = cos(x) at x = using a value…

A:

Q: Let f(x)=6x/sin x + cos x f'(−π)=

A:

Q: find the slope Of the followiny functions at the gruen point: at Xo to JL

A:

Q: Determine f'(x) for: Ax) = sin (5x - 2)

A:

Q: Q1) Show that: (b) (cosx) = -sinx =1+* (a) (1+x) =1+6x %3! (e) (VF) = (d) v1+ tan x

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: (sinx -) tan*(5x) Q3/ 1)- lim, 2)- limx-0 (3sin?x -sinx +1) x sin3 (2x)

A: There are multiple question. As per Bartleby policy Kindly ask other question separately.  Given…

Q: Which of the following functions listed below will result in differentiating f(r) = cosh(r) +e a…

A: Option A is correct.  If we differentiate for the first time we get f'(x) = sinhx - e^(-x)  Again…

Q: Prove that sin x can be approximated by x − (x^3/6) within 0.01 on the interval [-1,1].

A:

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

A:

Q: Use three-point midpoint formula to evaluate the first derivative of y = cot(x) at x = using a value…

A:

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: Let h(x) tan(5x + 7). Then %3D h'(4) is and h''(4) is

A: As in question it is not mentioned wheather we have to considered degree or in radian inside…

Q: Determine the concavity of the function f(x) = cos x^2 + sin x^2 + x^2 between x = -1.5 and x = -2.5

A:

Q: 1 lim (1 + sin²x)x

A: We have to solve the given limit: limx→01+sin2 x1x This is 1∞ indeterminate form of limit we know…

Q: Find f" (x) if f (x) = tan(x² − 1). ○ 2 sec² (x² - 1) ○ 2 sec² (x² − 1) (1 + 4x² tan(x² − 1)) ○ 2…

A:

Q: Let S(x) 9 sin x + 9 cos x "(x) 3= r(-)-

A: A function is given as fx=9sinx+9cosx. The objective is to find the first derivative f'x of the…

Q: Determine f(x) a. f(x) = 4 sin² (x - 2) b. f(x) = 2(cos x)(sec² x)

A: (a) The given function is f(x)=4sin2x-2 Find the first derivative…

Q: What are the intervals of monotonicity of f(x) = arctan (2(x-1)) - ln IxI ?

A:

Q: 5) f(x) = tan [In{sin(15x - 30)}] %3D

A: For this problem we have to apply derivation to each term.

Q: se backward-difference formula to evaluate the first derivative of y = cos(x) at - using a value of…

A: Backward difference formula for the first derivativeGiven

Q: List all intervals for which there are possible unique solutions (t-5)x''-ln(t)y'-y=et

A:

Q: Let f (x) = (10x + 6)(x – tan x). Then %3D - f'(x) =

A:

Q: Let f(x) = 6 sin ¹(x²). Then f'(x) equals 12x √1-x² 1 1- x4 6 /1-x² 12x cos−¹(x²) 12x √1 x4

A: The objective is to find the derivative of f(x).

Q: O find fx) if CoSx @ £(x)=. Sin X O flx) = x-4CSC x+2 Cot X © f(x)= (x).cotx 3- COSX. CSCX

A: SOLUTION-

Q: d dx [ 3+√√f(sin( sin(x)) cos(x) f' (sin(x)) 2√f(sin(x))

A:

Q: c) Sa* sin*x dx

A: To evaluate : The integral  ∫π43π4 sin4 x dx .

Q: Solve tan? (0) 1 on the interval (0, 7). || 0 = ||

A: