Elementary Function Derivitives Flashcards
What is the derivative of f(x) = x^n?
f’(x) = n*x^(n-1)
True or False: The derivative of sin(x) is cos(x).
True
What is the derivative of f(x) = cos(x)?
f’(x) = -sin(x)
Fill in the blank: The derivative of e^x is ______.
e^x
What is the derivative of f(x) = ln(x)?
f’(x) = 1/x
What is the derivative of f(x) = tan(x)?
f’(x) = sec^2(x)
True or False: The derivative of x^2 is 2x.
True
What is the derivative of f(x) = arctan(x)?
f’(x) = 1/(1+x^2)
What is the derivative of f(x) = sinh(x)?
f’(x) = cosh(x)
Fill in the blank: The derivative of f(x) = e^(ax) is ______.
a*e^(ax)
What is the derivative of f(x) = cosh(x)?
f’(x) = sinh(x)
What is the derivative of f(x) = log_a(x)?
f’(x) = 1/(x*ln(a))
What is the derivative of f(x) = sec(x)?
f’(x) = sec(x)tan(x)
True or False: The derivative of f(x) = x^3 is 3x^2.
True
What is the derivative of f(x) = cot(x)?
f’(x) = -csc^2(x)
What is the derivative of f(x) = arcsin(x)?
f’(x) = 1/sqrt(1-x^2)
Fill in the blank: The derivative of f(x) = x^n where n is a constant is ______.
n*x^(n-1)
What is the derivative of f(x) = f(x) = arccos(x)?
f’(x) = -1/sqrt(1-x^2)
What is the derivative of f(x) = csch(x)?
f’(x) = -csch(x)cot(x)
True or False: The derivative of f(x) = 1/x is -1/x^2.
True
What is the derivative of f(x) = x^1/2?
f’(x) = 1/(2*sqrt(x))
What is the derivative of f(x) = sech(x)?
f’(x) = -sech(x)tanh(x)
Fill in the blank: The derivative of f(x) = x^(1/n) is ______.
(1/n)*x^((1/n)-1)
What is the derivative of f(x) = arcsinh(x)?
f’(x) = 1/sqrt(1+x^2)
