Rates of Change and the Derivative
What is the slope of the tangent line to the graph of f(x)=x2 at the point (-2,4)
y-4=-4(x+2)
What is the derivative of the function f(x)=x2-5x
F'(x)=2x-5
What is the derivative of the following function: f(x)= 8x4 - 9x
f'(x)= 32x - 9
What is the derivative of 6/t5?
-30/t6
What is the derivative of x+cosx?
1-sinx
What is the instantaneous rate of change of the function f(x)=x2-5x at c=2
lim x->2=-1
What is the derivative of f(x)=(x)1/2 and what is its domain?
F'(x)=1/2(x)1/2
Domain:(0, infinity)
What is the derivative of ex
ex
What is the derivative of (1+x3)ex?
3x2ex+(1+x3)ex
What is the derivative of tanx?
Sec2x
What is the equation of the normal line to the graph of f(x)=2x+1 at the point (-2,4)
y-4=5/12(x+2)
Does f'(1) exists?
{-2x2+4, x<1; x2+1, x>1
Yes, f'(x)=-4
What is the derivative of the following function: f(x)=3x4 - 7x3 + 2x2 - 4
f'(x)=12x3 - 21x2 + 4x
What is the second derivative of secx?
secxtan2x + sec3x
What is the derivative of x3cotx?
3x2cotx-x3csc2x
What is the derivative of f(x)=2x2-3x-2 at x=2
lim x->2=5
What is the graph of the derivative f(x)=x^3
f'(x)=2x^2
What is the derivative of the following function: f(x)=5ex - 6lnx
f'(x)=5ex - 6/x
What is the derivative of (x2+1)/(2x-3)?
(2x2-6x-2)/(2x-3)2
What is the derivative of cosx/1-sinx?
1/1-sinx
What is the derivative of f(x)=(2x)1/2 at x=8. Then find the equation of the tangent line to the graph of f at the point (8,4)
y-4=1/4(x-8)
The surface are of a balloon is expanding as a function of time t according to S=S(t)=5t2. What is the rate of change of the surface area of the balloon with respect to time?
S'(t)=10t
What is the derivative of the following function: f(x)= ln(e7x)
f'(x) = 7
A ball is propelled vertically upward from the ground. The position function is s(t)= -4.9t2+29.4t. t is the number of seconds that elapse from the moment the ball is released. What is the velocity at t=1?
19.6m/s
What is the acceleration equation of 2+cost?
-cost