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)

Expert Solution

milcah answered 2 years ago

(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))

. 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

Suppose that f is a differentiable function with derivative f" (x) = (x − 3)(x +...

Suppose that f is a differentiable function with derivative f" (x) = (x − 3)(x + 1)(x + 5). Determine the intervals of x for which the function of f is increasing and decreasing Explain why a positive value for f" (x) means the graph f(x) is increasing For f(x) = 2x2- − 3x2 − 12x + 21, find where f'(x) = 0, and the intervals on which the function increases and decreases Determine the values of a, b, and...

1) Let f(x) be a continuous, everywhere differentiable function and g(x) be its derivative. If f(c)...

1) Let f(x) be a continuous, everywhere differentiable function and g(x) be its derivative. If f(c) = n and g(c) = d, write the equation of the tangent line at x = c using only the variables y, x, c, n, and d. You may use point-slope or slope-intercept but do not introduce more variables. 2) Let f(x) be a continuous, everywhere differentiable function. What kind information does f'(x) provide regarding f(x)? 3) Let f(x) be a continuous, everywhere differentiable...

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)

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 :)

Let f be a differentiable function on the interval [0, 2π] with derivative f' . Show...

Let f be a differentiable function on the interval [0, 2π] with derivative f' . Show that there exists a point c ∈ (0, 2π) such that cos(c)f(c) + sin(c)f'(c) = 2 sin(c).

For the following exercises, use the definition of derivative to calculate the derivative of each function. f(x) = 5π

For the following exercises, use the definition of derivative to calculate the derivative of each function.f(x) = 5π

Prove that if f, g are integrable, then the function (f(x) + cos(x)g(x))2is integrable.

If f and g are both differentiable functions. If h = f g, then h'(2) is: ___________________

If f and g are both differentiable functions. If h = f g, then h'(2) is: ___________________ Given the function: y=sin(4x)+e^-3x and dx/dt = 3 when x=0. Then dy/dt = ________________ when x=0. Let f(x) = ln (√x). The value of c in the interval (1,e) for which f(x) satisfies the Mean Value Theorem (i.e f'(c)= f(e)-f(1) / e-1 ) is: _________________________ Suppose f(x) is a piecewise function: f(x) = 3x^2 -11x-4, if x ≤ 4 and f(x) =...

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