Find the derivative of the function at the given number. f(x) = x2 - 8 at 0 f(0) = [-/1 Points] DETAILS SULLIVANCALC2 2.1.027. Find the derivative of the function at the given number. f(x) = x at 25 f'(25) [-/1 Points] DETAILS SULLIVANCALC2 2.2.053. Find the derivative of the function. 2 f(x) x² f'(x) =
Find the indicated derivative for the given function. f"(x) for f(x) = e = x2 {"(x) =
Question 2-Part B: How many inflection points for the function whose second derivative is f"(x) sin(3x)-cos(x2) for 0 < x < 3 Question 2-Part B: How many inflection points for the function whose second derivative is f"(x) sin(3x)-cos(x2) for 0
Using the definition of the derivative, find f'(x) for the following function. 3. f(x) = x2 + x - 1 the definition of the derivative f'(x) = lim f(x+h)-f(x) h h-0 What is the slope of tangent line to this curve at x = -1?
D1.1. Evaluate f'(a) by using the definition of derivative of a function f(x) = 4x2 + 3x – 5 at a = -2. [4 Marks] D1.2. (a) Find the derivative of y = 4 sin( V1 + Vx). (b) If y = sin(cos(tan(x2 + 3x – 2))), then find the first derivative. [3 Marks] D1.3. Using logarithmic differentiation, find the derivative of y = (sec x)+”.
Find the derivative of the function. f(0) = cos(02)
Suppose f(x, y) = x2 + y2. Find the directional derivative of the function f at the point P(1, -1) in the direction of 7 = -31 + 4. That is, find Dif(1,-1). 5 14 O 14 5 O 14 5 O 5 14
Apply the second derivative test to find the relative extrema of the function f(x)=ln(x2+x+1)
Find the directional derivative D−→ u f(x,y) of the function f(x,y) = x2 + 3xy + y3 where →− u is the unit vector given by angle θ = π 4. What is D−→ u f(1,1)?
Find the derivative of the following functions: (x2-1) f(x) = (x2 +1) f(x) = (x3 + 2x)3(4x + 5)2