Calculo DIFERENCIAL Flashcards
What is the derivative of a constant function?
The derivative of a constant function is 0.
What is the power rule for derivatives?
If f(x) = x^n, then f’(x) = n*x^(n-1).
True or False: The derivative of sin(x) is cos(x).
True.
What is the derivative of cos(x)?
The derivative of cos(x) is -sin(x).
Fill in the blank: The derivative of e^x is _____ .
e^x.
What is the product rule for derivatives?
If u(x) and v(x) are functions, then (uv)’ = u’v + uv’.
What is the quotient rule for derivatives?
If u(x) and v(x) are functions, then (u/v)’ = (u’v - uv’)/v^2.
What is the derivative of ln(x)?
The derivative of ln(x) is 1/x.
True or False: The derivative of tan(x) is sec^2(x).
True.
What is the chain rule for derivatives?
If y = f(g(x)), then dy/dx = f’(g(x)) * g’(x).
What is the derivative of x^3?
The derivative of x^3 is 3x^2.
Fill in the blank: The derivative of a constant k is _____ .
0.
What is the derivative of a polynomial function?
Differentiate each term using the power rule.
True or False: The derivative of a linear function is always a constant.
True.
What is the derivative of 5x^4?
The derivative is 20x^3.
What is the derivative of sinh(x)?
The derivative of sinh(x) is cosh(x).
What is the derivative of cosh(x)?
The derivative of cosh(x) is sinh(x).
Fill in the blank: The derivative of a function gives the _____ of the function at a point.
slope.
What is the derivative of a constant times a function?
If k is a constant and f(x) is a function, then (kf)’ = kf’.
True or False: The derivative of x^n is n*x^(n-1) for any real number n.
True.
What is the derivative of the exponential function a^x?
The derivative is a^x * ln(a).
What is the derivative of the inverse function f^(-1)(x)?
The derivative is 1/f’(f^(-1)(x)).
What is the second derivative of a function?
The second derivative is the derivative of the first derivative.
What is the derivative of x^2 + 3x + 5?
The derivative is 2x + 3.
