Solve the questions given below using the Fundamental Theorem of Calculus. r9(x) If f(x) = 1 rcos a dt, where g(x) = | (1+ sin(t²)] dt, find f'(}). V1+t3

Q: If f(x)=2 sin x/1+cos x, then f′(x) =    f′(4) =

A: We have to find

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. Given f(x)=x-6, determine whether f'(6) exists.

A:

Q: The derivative of f(x) = 5x – Vx + (sin)x – e² -

A: Given; f(x)=5x4-x1/3+[sin(π/2)]x-e2

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: Show that, for any constant k, f(x)' dxL k f'(x) k

A: To show: For any constant k, ddxf(x)k = f'(x)k

Q: x () - (-). y (1) J

A: Givenf(t)=sect   We are required to find f''π4

Q: (In 2z - 1) – 25z(In Given the function f(z) = f t In t – tdt then by using the fundamental theorem…

A: Given problem:-

Q: Given: ¬A → (CA D) ... Premises: А— В ¬B Prove C. Match the correct rule of inference to the number…

A:

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: If SeF dr = [c(-5x + 3y² ) dx + (x³y) dy, what is F? %3D F =

A:

Q: If f(x) = |"(9 – t2)e dt, on what interval is f increasing? (Enter your answer using interval…

A: The function is fx=∫0x9-t2et2dt By second fundamental theorem of Calculus, f'x=9-x2ex2. Set the…

Q: 3. If f(x) = sinx ex find f'(0).

A: fx=sinxex

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: A 2xe ²x² B Xex² Ⓒ2e+² D 2xex² Let f(x)= ex², find f'(x)

A: given  f(x)=ex2d dx(ex)=exd dx(xn)=nxn-1

Q: Suppose you are standing at a point on the equator of a sphere. parameterized by spherical…

A: Suppose you are standing at a point on the equator of a sphere, parameterized by spherical…

Q: Let f (x) 6x + 3 Then the derivative of f is 2х— 1 Ax + B f'(x) where (2x – 1)C' %3D B = C = || ||…

A:

Q: (2) GIVEN: f.R- R, Sx) = x²(3x– 1). Find f'(x) in factored form.

A:

Q: answer. 3. Given f(x) = ln(5x + 3)2, find f'(0), Your answer should be exact-no %3D decimals!

A:

Q: Given that: f(-3) = 2, f'(-3) = 4, g(-3) = 9, g'(-3) = 7, calculate the following: (fg)'(-3) =…

A:

Q: 3x t²- - 1 Let F(x) = √ 12 + 1 dt. 2x (i.e. the derivative of F(x) with respect to x). What is…

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Q: Suppose that f(x + h) – f(x) = 7hx? – 8hx + 5h²x – 3h? – 7h³. Find f'(x).

A: The quotient difference formula is given as, f'x=limh→0fx+h-fxh it is given that…

Q: 7. If in an inner product space, (x, u) =(x, v) for all x, show that u = v.

A:

Q: [2, 03 b) If f(t)={ , find L{S(1)}.

A:

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

A: Given

Q: If f(x) = t*dt then f'(x) =

A:

Q: Find F(s). F(s) = L {tu(t = 3)}

A: detailed solution is given below

Q: Let f(x) = x°e*. Find f '(x).

A: Product rule:d(uv)dx=udvdx+vdudx