1)
we have
so,
by the definition of derivative,
at x = -9
at x = 0
at x = 9
2)
so,
by the definition of derivative,
at t = -2,
at t = 4,
at t = sqrt(6),
3)
4)
at t = -6,
Using the definition, calculate the derivative of the function. Then find the values of the derivative...
Question Help specified Using the definition, calculate the derivative of the function. Then find the values of the derivative as - f(-2)-0 f(x) = 5 + x2: f'(-2). (O).(2) 0-0 (2)
Please circle all 4 answers in order. Thanks. the derivative as specified. Using the definition calculate the derivative of the function. Then find the values of pe=Q f(x) = 1 + x2, f'( -8), f'(o), P (9) p(-8)=0 f(0) = 0 P(9)=
dy For the following composite function, find an inner function u = g(x) and an outer function y=f(u) such that y=f(g(x)). Then calculate dx y=tan (2x) Calculate the derivative of the following function. y = (5x - 19) dy Carry out the following steps for the given curve. dy a. Use implicit differentiation to find dx b. Find the slope of the curve at the given point. x +y = 337;( - 4,3) a. Use implicit differentiation to find b....
14. x Find the derivative of the function using the definition f(x) = x + 3 15. The equation of motion of a particle is s = p - 27t, where s is in meters and t is in seconds. (Assume 10.) (a) Find the velocity and acceleration as functions of t. (b) Find the acceleration after 4 s. (c) (c) Find the acceleration when the velocity is 0. 16. Find the points on the curve y = 2x3 +...
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...
find the derivative Find the derivative of the function. y=9 eX + e 2x dy dx Find the derivative of the function. y=9 eX + e 2x dy dx
7*). Using this definition, Derivative of a function f (x) can be expressed as f'(x) = lim ** find out the first order derivative (f'(x)) of the following functions: h 0 h f(x) = 2x2 + 4 f(x) = 2x (4 points) (4 points)
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. y=5 e 2x2-3 dy 80 e 2x2x2 * + 20 e 2x2 X X Try again. Differentiate the exponential using the Chain Rule. to le 9(x) = g(x)g'(x) OK Find the derivative of the given function. y = (3x2 + 5x) -7x e -7x -7x y' = -21 e -7xx2 -29 +5e (Type an exact answer.) x X That's incorrect. The product rule states that if f(x) = u(x)•v(x), and if both u'(x) and...
ame f(x) If f(x) is a differentiable function, find an expression for the derivative of y= X Choose the correct answer below dy 7f(x)-xf'(x) O A. dx 8 X xf (x) 7f(x) dy O B. dx 8 X dy xf(x) 7f(x) O C. dx 8 X 7f'(x) xf(x) dy O D. dx 8 X ame f(x) If f(x) is a differentiable function, find an expression for the derivative of y= X Choose the correct answer below dy 7f(x)-xf'(x) O A....