Using the definition of an anti-derivative, prove that x (ln x)3 – 3x (ln x)2 +...

Using the definition of an anti-derivative, prove that

x (ln x)³ – 3x (ln x)² + 6x (ln x) – 6x

is an anti-derivative of (ln x)³ (must show all work)

Expert Solution

milcah answered 2 years ago

. Let f(x) = 3x^2 + 5x. Using the limit definition of derivative prove that f...

. Let f(x) = 3x^2 + 5x. Using the limit definition of derivative prove that f '(x) = 6x + 5 Then, Find the tangent line of f(x) at x = 3 Finally, Find the average rate of change between x = −1 and x = 2

Let f(x) = −3+(3x2 −x+1) ln(2√x−5) (a) Find the derivative of f. (b) Using the derivative...

Let f(x) = −3+(3x2 −x+1) ln(2√x−5) (a) Find the derivative of f. (b) Using the derivative and linear approximation, estimate f(9.1).

prove using the definition of derivative that if f(x) and g(x) is differentiable than (f'(x)g(x) -...

prove using the definition of derivative that if f(x) and g(x) is differentiable than (f'(x)g(x) - f(x)g'(x))/g^2(x)

(a) State the definition of the derivative of f. (b) Using (a), prove the following:d/dx(f(x) +g(x))...

(a) State the definition of the derivative of f. (b) Using (a), prove the following:d/dx(f(x) +g(x)) =d/dx(f(x)) +d/dx(g(x))

what is the derivative of y=e^x/(3x+1)^4(x+1)^3

Using the epsilon-delta definition prove Lim of x^2 =4 when x approaches 2

Two questions: 2) Use the limit definition of the derivative to find the derivative of f(x)=...

Two questions: 2) Use the limit definition of the derivative to find the derivative of f(x)= x^3 - 9x 3) Using limits, find an equation of the line tangent to the function of g(x)= 4/x^2 at x= -2 Show All Work please! thank you :)

Find the derivative Y=ln(3-2x)

1a. Find the equation of a tangent line to the curve f(x) = ln(2−x)/x + 3x...

1a. Find the equation of a tangent line to the curve f(x) = ln(2−x)/x + 3x at the point (1, 3). 1b. Suppose the following function is defined implicitly by the equation, Find dy/dx x^2 − 3y^2 + 6e^x = 4x^2y + 5 2. Using only the definition of derivative as a limit, calculate f(x) where f(x) = 1/x − 5 3. One thousand dollars is invested at a rate of 3% a) How much money will be in the...

Compute the derivative of each function a.) f(x)= x5/2 - 3x2/3 b.) f(x) = 3x- log7x+7...

Compute the derivative of each function a.) f(x)= x5/2 - 3x2/3 b.) f(x) = 3x- log7x+7 c.) f(x)= 8x6-5x3+3x2-11x+7

Question