4) (5 points) Use the definition of the differentiation to find the derivative of f(x) x2...
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)+”.
5. Use the limit definition to find the derivative of f(x) = V3x + 2. (6 points) 6. Find the derivatives of the following functions. Do not simplify after taking the derivative. 5 points each a. f(x) = (4x2 +1) c. h(x) = arcsin(3x2+ 2x-1) b. h(x) = 3sec(x2)
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?
(4) Use the definition of derivative (not any shortcut formulas) to find the derivative of the following function: f(x) = x2 + 8x +9
11. a) Find the derivative of f(x) by using the definition of derivative: lim f(x+4x) - f (x ) Ax0 Ar f(x) = 4x² +8 Make sure you show all your work clearly and neatly!!! If steps are not clearly written you will not receive any credit. (9 points) f'(x) = b) Check your answer from part (a) by finding the derivative of f(x) = 4x² +8. (1 pts) f'(x)= c) What is the instantaneous rate of change of the...
please help me with these. Thanks.
4. Use implicit differentiation to find an equation of the tangent line to the graph y2 + In xy = 2 of at the point (e, 1) )(-5) using formula for the derivative of the inverse 5. Consider f(x) = x + 3x - 1. Find (f function. 6. Consider the following function and its inverse f(x) = x-4 f(x) = x2 +4, point (5,1) point (1,5) x20 a) Graph both functions on the...
3. Let f(x) = (a) (15pts) Use the definition of the derivative to find f'(5). (b) (5pts) Write the equation of the tangent line at (5,3).
Cal 4
, ) and use this to 6. Let f(x,y) = x2 + y2 + 2x + y. (a) Find all critical points of f in the disk {(x,y) : x2 + y2 < 4). Use the second derivative test to determine if these points correspond to a local maximum, local minimum, or saddle point. (b) Use Lagrange multipliers to find the absolute maximum/minimum values of f(x, y) on the circle a2 +y -4, as well as the points...
5. (a) Use the definition to find the function's derivative and then evaluate the derivative at the indicated point. 2 f(x)= X=1 2x + x (5 Marks)
need steps
14. Use logarithmic differentiation to find the derivative of f(x) = n(x) at = e.