Derivative of familiar function
Given f(x) = 2cot(x) find f'(x)
-2csc^2 (x)
given the function y = -x^5 - x^-2 + 1/3, find d2y/dx2
d2y/dx2 = -20x^3 - 6x^-4
Whats the Constant rule
d/dx c = 0
Given the function f(x) = (1 - 8x^3 - 10x^2)(-1-4x^3), find f'(x) in any form
f'(x) = (-24x^2 - 20x)(-1-4x^3) + (-12x^2)(1 -8x^3-10x^2)
Given y = -3sec(x), find dy/dx
dy/dx = -3sec (x) tan (x)
whats the derivative of =
f(x) = 8√x - x^6/3 + 2𝝅^5
f'(x) = 4x^ -1/2 - 2x^5
Whats the product rule
d/dx(uv) = u * dv/dx + v * du/dx
Given f(x) = 3tan(x), write the equation of the line tangent to y = f(x) when x = 5π/6
y + √3 = 4(x - 5π/6
y = -3tan(x), find dy/dx
dy/dx = -3sec^2(x)
given the function f(x) = 4/3x^-2 + x^-1 + x^3 - 1/24x find f''(x) in simplified form
f''(x) = 8x^-4 + 2x ^-3 + 6x
quotient rule
v du/dx - u dv/dx / v^2
given f(x) = 4cos(x) write the equation of the line tangent to y = f(x) when x = 5π/4.
y + 2√2(x - 5π/4)
For the following equation, evaluate f(-2)
F(x) = -x^3 + 3x - 5
f(-2) = -9
Given the function y = -2/3x^4 - 3/10x^6 - 1/3x^-3find d2y?dx2 in simplified form
d2y/dx2 = -8x^2 - 9x^4 -4x^-5
sum and difference
d/dx u + v = du/dx + dv/dx
For the function f(x) - x^2 - x -1, find the slope of the secant line between x = -1 and x = 2
-2
For the following equation, find f'(x)
f(x) = -6x^4 + 8x - 7
f'(x) = -24x^3 + 8
given the function y = -1/3 x^4 - 1 - 1/4x^-3 - 4x^2
find d3y/dx3 in a simplified form
d3y/dx3 = -8x+ 15x^-6
Constant multiple rule
d/dx cu = c * du/dx
Given the function f(x) = 2x^4, write an expression that represents the derivative of ff using the limit shown below. You do not have to simplify your answer.
lim h - 0 2(x+h)^4 - 2x^4/h