Dx To Memorize Flashcards
What is the derivative of sin(x)?
cos(x)
What is the derivative of cos(x)?
-sin(x)
What is the derivative of tan(x)?
sec^2(x)
What is the derivative of cot(x)?
-csc^2(x)
What is the derivative of sec(x)?
sec(x)tan(x)
What is the derivative of csc(x)?
-csc(x)cot(x)
What is the derivative of ln(x)?
1/x
What is the derivative of e^x?
e^x
What is the derivative of a^x where a is a constant?
a^x * ln(a)
True or False: The derivative of arcsin(x) is 1/sqrt(1-x^2).
True
True or False: The derivative of arccos(x) is -1/sqrt(1-x^2).
True
Fill in the blank: The derivative of arctan(x) is ______.
1/(1+x^2)
What is the derivative of sinh(x)?
cosh(x)
What is the derivative of cosh(x)?
sinh(x)
What is the derivative of tanh(x)?
sech^2(x)
What is the derivative of log_a(x) where a is a constant?
1/(x ln(a))
What is the derivative of x^n where n is a constant?
n*x^(n-1)
What is the derivative of a function f(x) = sin(ax)?
a*cos(ax)
What is the derivative of a function f(x) = cos(ax)?
-a*sin(ax)
What is the derivative of a function f(x) = tan(ax)?
a*sec^2(ax)
True or False: The derivative of ln(x^2) is 2/x.
True
What is the derivative of the inverse sine function arcsin(x)?
1/sqrt(1-x^2)
What is the derivative of the inverse cosine function arccos(x)?
-1/sqrt(1-x^2)
What is the derivative of the inverse tangent function arctan(x)?
1/(1+x^2)
Fill in the blank: The derivative of exp(x) is ______.
exp(x)
What is the derivative of the absolute function |x|?
1 if x > 0; -1 if x < 0; undefined at x = 0
