Defining The Derivative
What is the limit that gives an expression which calculates the IROC at any given x-value? (hint: using h)
f'(x) = lim h->0 (f(x+h)-f(x))/h
What is the formula for calculating the average rate of change of a function over an interval?
(f(x)-f(a))/(x-a)
Use the power rule to find the derivative of y = x^84
dy/dx = 84x^83
Find the derivative of g(x) = sin(x)/x
g'(x) = ((x)(cos(x))-sin(x))/(x^2)
What is the expression for the product rule?
h'(x) = (f')(g) + (f)(g')
Find the derivative
f(x) = 6x^2 - 33x + 18
f'(x) = 12x - 33
Find the IROC of f(x) = x - x^2 at x = -1
3
y' = (-4/x^5)
Find the equation of the tangent line of f(x) = (sinx)/(cosx) at x=(pi/3)
y-sqrt(3) = 4(x-(pi/4))
Find the derivative of f(x) = (2x-3)(sinx)
f'(x) = 2sinx + (2x-3)(cosx)
Find the derivative
y = sqrt(5x+2)
dy/dx = 5/2(sqrt(5x+2))
Find the function that we are working with, from the limit: lim x -> (pi/2) (sin(x)-1)/(x-(pi/2))
f(x) = sin(x)
Use the power rule to show how you would find the derivative of x^n
f'(x) = n(x)^(n-1)
Find the derivative of f(x) = (2x+4)/(3x+2)
f'(x) = (-8)/(3x+2)^2
Find the equation of the tangent line for g(x) = -2xe^x at x = 0
y = -2x
Create an equation of the tangent line of f at the given point (leave in point slope form)
f(7)=5, f'(7)=-2
y-5=-2(x-7)
Find the average rate of change of a(x) = ln(x) on the interval 2 <= x <= 7
0.251
Find dy/dx of y=x^pi
dy/dx = pi(x)^(pi-1)
Find the derivative of f(x) = (e^x)/4sinx
f'(x) = ((e^x)(sinx-cosx))/(4x)(sin^2)
Find the equation of the tangent line for f(x) = 8(sinx) (cosx) at x = pi/3
y-2(sqrt(3))=-4(x-(pi/3))
What is the equation of a tangent line?
y-y1=m(x-x1)
Find the AROC of f(x) = sin(x)ln(x) on the interval 1<=x<=a
(sin(a)ln(a))/(a-1)
When do the two following functions have parallel tangent lines?
f(x) = x^2
g(x) = x^5
x=0 & x= third root(2/5)
What is the expression for the quotient rule?
h'(x) = ((g)(f')-(f)(g'))/(g^2)
Find the derivative of h(x) = (1/x + 1)(2x^2 - 5)
h'(x) = 5/x^2 + 4x + 2