dt 7. For x > 0 define L(x) = ft. Show that L(xy) = L(x) + L(y). Show that L'(x) = 1/x. Show that L is the inverse to the exponential function E(x) defined by the power series E(x) = Σ0x² /k! k=0 (Hint: Consider the derivative of the composition L o E. Be careful with domains and ranges. You may use any properties of the function E that we developed in the lectures.)

Q: Compute the derivative f'(x) for f(x) = log(x*) sin(x³).

A: Topic - derivative

Q: For each of the given functions f(z), find the derivative (f)'(c) at the given point c, first…

A:

Q: Find f(x) for the following function. -In x f(x) = 3/¹¹ a 01 3 02 O In x-2 Vn VE -2. (1 - ln x) In…

A:

Q: LET 9 (3)=4₁ g (3)=-1 FIND H (3) For H(X) = xg(x) 5x-6 FUNCTION

A: solution is given below..

Q: Let f(x) = z and g(a) = f (2). Find g' (x) by findingf (x) and then taking the derivative. O g' (x)…

A:

Q: At time t = 0, a storage tank is empty and begins filling with water. For t > 0 hours, the depth of…

A:

Q: 16. For h(x): = a. f'(x) 8'(x) f(x) g(x) b. f'(x)g'(x) [g(x)]² which expression represents h'(x)? 1K…

A:

Q: Use the information in the table to find h'(a) at the given value of a. h(x) = (- 2 f(x) ;a = 3 g(x)…

A:

Q: -7/3 Find g'(x) for g(x)=x

A: Power rule of derivative:

Q: Let f (x)  = xsqrt(x). Find f '(4).

A: Since you have asked multiple question As per our policy, we will solve the first question for…

Q: - 4/9 Find g'(x) for g(x)=x g'(x) =

A:

Q: - 3/7 Find g'(x) for g(x) = x g'(x) =

A:

Q: For all x > 1, if ƒ (x) = fï ½ dt, then ƒ¹ (x) = = ○ In(x - 1) о ех x 01

A: