Derivatives
Find y' if y = (3x - 9)4. Give your answer in as simplified a form as possible.
12(3x - 9)3
Find the derivative of y = 3x(sin x)
y' = 3x(cos x) + 3(sin x)
What is the derivative of y = (x2-2)2 at x=2?
16
Find the slope of the tangent line to y = ln(3x) at x = 2.
The slope is 1/2
Find the equation of the tangent line to y = ln(x3) at x=e.
y-3=3/e (x-e) or just y = 3x/e
Find the derivative of f(x) = e-x at x=0.
-1
f(x)=eln(cos(5x-3)). Find f'(x)
f'(x)=-5sin(5x-3)
Find the derivative of f(x) = ln(3x+2)
f'(x)=3/(3x+2)
f(x) = 1/(1-cos x)3. Find f'(pi/3).
-24*sqrt(3)
If the position of an object on the x-axis is given by x(t) = t*cos(3t) meters at time t seconds, then what is the velocity of the object when t = pi/2?
3pi/2 meters per second
Find the derivative of f(x) = cot(5x)
f'(x)=-5 csc2(5x)
Find the derivative of y = 1/(6x2-3)5. Give your answer in simplified form with no negative exponents.
y'=-60x/(6x2-3)6
Find y' if y = sin2(9x2 + 4)
What is 36x*sin(9x2+4)*cos(9x2+4)?
f(x)=ln(x2(4-3x)3). Find f'(1)
f'(1)=-7
What is the rate of change of f(t) = t2ln(2t-3) at the moment that t = 2?
8 units of f per unit of t
f(x)=(e3x+1)3. Find f'(0)
36
Find the slope of the tangent line to f(x) = (2ex + 5)/ex when x = 0.
What is -5?
f(x) = sin3(4e-x) Find f'(x)
-12e-x sin2 (4e-x)*cos (4e-x)
For what value or values of x does f(x) = x ln(x) have a horizontal tangent line?
What is x=e ?
What value of x does f(x)=xe-2x have a horizontal tangent line?
What is x = 1/2 ?
Find the derivative of f(x) = 3sec2(5x) in as simplified form as possible.
f'(x)= 30sec2(5x)tan(5x)
f(x)=1/[(ln x)1/2]. Find f'(e4)
-1/(16e4)
y = ln(x1/2)/x. Find y'(e).
y'(e)=0
If y1/2 = ln(ex(2x-3)). Find y'(2)
12
For what values of k does the tangent line to y = ln(x) at x=k have a y-intercept of (0,1)?
k = e2