Directions: Use the Rules of Differentiation to differentiate the following functions. Simplify, if possible. 1.g(x) 3 2х3 + 6х — 2 2. h(x) = (3x + 2)² x2 3. i(x) X-1
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Numbers 1-3 only.
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- What is the composition of two functions, fg ?Use the information about values of the functions and their derivatives to calculate G'(2), where G(x) = (x)g(x)f(x). f(2) = 9 f'(2) = -11 g(2) = 14 g'(2) = -4Use implicit differentiation to find y′ for the equation below and evaluate y′ at the indicated point. y^2+6y+9x=0; (-3,3)
- Use implicit differentiation to find y', and then evaluate y' for x^2 - 3x^3 + 8 = 0 at the point (2,4)find the derivatives and simplify f(x)=1/x (A) Find f ′(x) using the quotient rule, (B) Explain how f ′(x) can be found easily without using the quotient rule.Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. (Simplify your answers completely.) f(x) = 6 − 9x Step 1: f(x + h) = Step 2: f(x + h) − f(x) = Step 3: f(x + h) − f(x) h = Step 4: f '(x) = lim h→0 f(x + h) − f(x) h
- A. Find the equation of the tangent line to the curve y=(x-1)^ 5 (x+4)^2 at the point (2,36). The equation of the tangent line to the curve at the given point is y=_________ B. Differentiate the function. y= [(2x^2+4x+3)(x-9)]^2Find the derivative of the function using the definition of derivative. g(t) = 7/(t^1/2) g'(t) =? State the domain of its derivative. (Enter your answer using interval notation.)Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. (Simplify your answers completely.) f(x) = 10 Step 1: f(x + h) = Step 2: f(x + h) − f(x) = Step 3: f(x + h) − f(x) h = Step 4: f '(x) = lim h→0 f(x + h) − f(x) h =