If In = f(In x)" dx, show that In = x(lnx)" - nln-1. Hence find f(In x)³ dx.

Q: Let F(x) = f(xf (x²)). Suppose that ƒ(4) = 6, ƒ'(4) = 1, and ƒ'(12) = 5. Find F'(2).

A: Given, .Given,  f(4)=6, f'(4)=1 and f'(12)=5.

Q: Find d can'(x²cosbx) clx

A: To find:- Derivative of tan-1(x2 cos(x))

Q: Find f'(x) for f(x) = ln(3x² – 5x + 6). f'(x) = Preview

A: f(x)=ln3x2-5x+6f'(x)=ddxln3x2-5x+6f'(x)=13x2-5x+6ddx3x2-5x+6  [chain…

Q: Find f'(0) for f(x) x = 0. 0,

A:

Q: If f(x) = ln(x + ln(x)), what is f'(1). Show all work.

A:

Q: Let f(x) = x + 12 f-'(x) = %3D 1.

A: Let's say y = f(x) A function g is said to be inverse of a function f, if g(y) = f(x) Procedure to…

Q: Given f(x)=(6x+9)^4, what is f'(x) when x=19?

A:

Q: If Jo flx)dx= 31 and Jo gixldxX=16. find So'[ 4f (X\ + 6glx\] dx

A:

Q: If f(x) = 6 + Find f'(3). X 3 x² " find ƒ'(x).

A:

Q: Let f(x) - 6e* +2 + e'. f'(0) =

A: The given function is f(x)=-6ex+2+e1

Q: Let f(x)=100/5+2e-0.01x. Find f'(x).

A: Write the given function using exponent.

Q: f(x)= (x^3 +x)^4  a. find f'(x)    b. Find f''(x)

A: Given function

Q: - ((x3 + x)sech(In x)) = dx EX)-

A: To find  ddx(x3+x)(sech(ln x) We use product rule  d(uv)=udv+vdu Let  u=x3+x,     v=sech(ln…

Q: do implicit diff for thi with respect to x (xy)^(1/2) = 4 + x^(2)y

A:

Q: 2x + 3 f(x) = In %3D 7r – 7 f'(x) =

A:

Q: Let f f(x) dx = -3, f¹ f(x)dx = -4 and g(x)dx = 6 and ¹ g(x)dx = 2. Then evaluate * (7 f(x) — 28(x)…

A:

Q: Suppose f'(x) = sin(4x²). d f(5x)=[ dx d ƒ(2x5) dx

A:

Q: Suppose f(x)=ln((ex2)/(x-6)7). Find f'(x)

A: We have to find f'(x).

Q: Use x = e to explain why dx (In x) = = -, for x> 0.

A: To differentiate x=ey, with respect to x, use the exponential function rule, ddxef(x)=ef(x)ddxf(x).…

Q: Consider h(x)= {3x^2 +1, if x3. What is h'(3)?

A:

Q: Let f(x)=(x+4/x+2)^5 find f'(x).

A:

Q: find f'(t) for f(x)=x/8x-8

A: We will need the quotient formula to find f'(x) Assume u and v, then find u' and v'

Q: Find the interval on which f(x) =x'e is increasing.

A: We find f'(x) using the product rule

Q: Isn't the ln function supposed to have absolute brackets? like ln|y-1| instead of ln(y-1)?

A: Given differential equation .