Differentiate the following to the appropria g(x) =+5x 8(x): -5x 2.1 4 X' f(x) =(2x+1)(3x² – x) h(t) = sin(7t) 2.2 2.3 2x+1 q(x) = JAx +1 2.4

Q: Suppose that f(x + h) – f(x) = 5hx + 8h – 6h². Find f'(x). f'(x) =

A: Given: fx+h-fx=5hx+8h-6h2, To find: f'x.

Q: If f(x) = cos(2x) then find II f (t|4)

A: Given query is to find the Indicated derivative.

Q: 4. Find (f-1)'(1) if f(x)=x' +8x+sin(3.x) а. Find (f-1)'(2) if f(x)= Vx' +x +xr+1 b.

A: To find the derivative of the inverse of a function

Q: Differentiate the following function. f(x) = (x+2) e-6x +1 f'(x) = (Type your answer in factored…

A:

Q: 2. Explain how the maxima and minima of f(x)=sinx, gix)=sin(2x) and hox)=sin(3x) affect the shape of…

A: (2) To Explain: How the maxima and minima of sinx, sin2x, sin3x affect the shape of the graph of…

Q: Verify the following properties for ƒ(x) = sin x and p3(x) = x - x3/6:                    ƒ(0) =…

A: We first find the derivatives

Q: Find the GS for x³y"" + 6x²y" + 4xy' — 4y = 1 − x − 2x² -

A: Solution:-

Q: If f(t) = e-t3 – 2 sin 2t determine L{f" (t)} %3D

A: Formula Used: L{eattn}=n!(s-a)n+1L{sin at}=as2+a2L{f''(t)}=s2L{f(t)}-sf(0)-f'(0)

Q: Suppose (=/3) = 3 and f '(m/3) = -7, and let g(x) = f(x) sinx and h(x) = (cos x)/(x). Find the…

A: So, Again, if , Then

Q: 1. f (x² + 1)(x² + 3x) dx

A: To evaluate the given integral.∫x2+1x3+3x4dx

Q: If 7'(t) = (cos t, e2t, 3t²) and r(0) = (3, 1, –2), find the function 7 (t).

A: Given. f'(t) = (cos t , e2t , 3t² ) To calculate the vector function are we need to integrate the…

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: Find x and y for which the following equation is satisfied: x+2 = - 5+i i-5

A:

Q: Find the derivative of the following functions a) f(x) = 1 + x² + = 160 1x x6 I b) F(X) x4-3x+1 √x…

A:

Q: For f(x)=In(cos(x)), what is

A:

Q: Find the differential of the following function: a) f(x) = x (2x³ + 9x)5 2t b) f(t) = (₁²₂)4 1-t2

A:

Q: . If f(x) = V4x – 7, find f'(x).

A: we have ;  f(x)=4x-7;  we have to find f-1(x)

Q: Suppose that f(x) 2 4x Find f'(x).

A: use quotient rule for differentiation

Q: et ƒ(x) = 3x² cos(4x). ='(x) = −12x² sin(4x) + 6x cos(4x) (2) = 17.245 "(2) = =

A:

Q: 4. x(x² – 1)² dx

A: Solution:

Q: Find f. f(t) = f'(t) sec(t) (sec(t) + tan(t)), -2-√2 x Need Help? Read It Watch It - 1/2 < t < 1/₁ (…

A:

Q: If f(x)= cos(4x) Plot the function from (x=0) to (x=180)

A:

Q: If f(x) + x²[f(x)]4 = 18 and f(1) = 2, find f'(1). f'(1) =

A: Given

Q: Find f. 13 f"(x)=x³+ sinhx, f(0) = 4, ƒ(2)= 5

A:

Q: 4. Consider f(x) = 6 + (x+3) ²/³. Find the extrema of this function using the first derivative test.

A: We have to find extrema by first derivative test.

Q: If f (x) = 3x + 5 and g(x) = x³,finc а. (f + g)(x) b. (f/g)(x) c. f(g(x)) с. d. (f°f)(x)

A:

Q: Let f(x) -9x(sin(x) + cos(x)). Find the following: 1. f'(x) = -9x cos(x) +9x sin(x) – 9 sin(x)-9 cos…

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Q: Determine f,(x); f(x) = cos(2x³ +n²)

A:

Q: Show that J−1/2(x) = √2/πx co

A: Bessel functions are a family of mathematical functions that arise in many areas of physics and…

Q: Differentiate the given function: f(x) = In(2r³ – 5æ) 6x² – 5 A f'(x) = 2x3 – 5x 1 ® f'(x) = 2x3 –…

A: