C6
Derivatives
of Basic Functions
Derivatives
of Basic Functions
f(x) = sin(x)
What is f'(x)?
f'(x) = cos(x)
What is the product rule?
h(x) = f(x)g(x)
What is h'(x)?
h(x) = (3x2)2+2
h'(x) = 2(3x2) * 6x
[C4]
f(x) = (x2-9) / 3-x
Using the limit definition, what is the derivative of f(x) as x approaches 3?
f'(3)= -1
f(x) = cos(x)+2x
What is f'(x)?
f'(x) = -sin(x)+2
What is the quotient rule?
h(x) = f(x)/g(x)h'(x) = [ g(x)f'(x) - g'(x)f(x) ]/ g(x)2
What is h'(x)?
h(x) = (x+2)2 + 3(x+2) +5
h'(x) = 2(x+2) + 3
h'(x) = 2x+7
[C3]
What is the tangent line of f(x) at x = 3?
f(x)= x2+x-2
y=7(x-3)+10
f(x) = tan(x) - sin(x) + cos(x)
What is f'(x)?
f'(x) = sec2(x) - cos(x) - sin(x)
What is h'(x)?
h(x) = (3x2 + 2x + 1) (x2 + 2x + 3)
h'(x) = (x2+2x+3)(6x+2) + (3x2+2x+1)(2x+2)
h'(x) = 12x3+ 24x2 + 28x + 8
What is h'(x)?
h(x) = sin(3x2)
h'(x) = cos(3x2) * 6x
[C5]
What is the average rate of change for f(x) from 0 ≤ x ≤ 1
f(x) = 4x3-2x2+5x-2
7
f(x) = cot(x) - cos(x) + 5x2
What is f'(x)?
f'(x) = -csc2(x) + sin(x) +10x
What is h'(x)?
h(x) = [(1/csc(x)) / (1/cos(x)) ] + 2x2
h'(x) = cos2(x) - sin2(x) + 4x
What is h'(x)?
h(x) = √(tan(x)) + 3 tan(x) + 1
h'(x) = (1/ [2 √tan(x)] + 3)(sec2(x))
What is the instantaneous rate of change for f(x) when x = 1
f(x) = 4x3-2x2+5x-2
13
f(x) = sec(x) - csc(x) + cot(x) + tan(x)
What is f'(x)?
f'(x) = sec(x)tan(x) + csc(x)cot(x) - csc2(x) + sec2(x)
h(x) = sin(x)cos(x) / 3x2 + 5x + 2
h'(x) = ( (3x2+5x+2)(cos^2(x) - sin2(x)) - (6x+5)(sin(x)cos(x) ) / (3x2 +5x +2)2
What is h'(x)?
h(x) = 3sin2(x)+5sin(x)+2
h'(x) = (6sin(x)+5)(cos(x))
[C8]
What is h'(x)?
h(x) = sin(cos(tan(2x)))
h'(x) = cos(cos(tan(2x))) * -sin(tan(2x)) * sec2(2x) * 2