Calculus: Derivative Rules
Mastering derivative rules is fundamental to success in calculus. This flashcard deck provides 15 essential rules and common derivatives, perfect for quick review or solidifying your understanding. Focus on these core concepts to build a strong foundation for more advanced topics.
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What is the derivative of a constant?
0.
What is the power rule?
d/dx xⁿ = n·xⁿ⁻¹.
What is the constant multiple rule?
d/dx [c·f(x)] = c·f′(x).
What is the sum rule?
The derivative of a sum is the sum of the derivatives: (f + g)′ = f′ + g′.
What is the product rule?
(fg)′ = f′g + fg′.
What is the quotient rule?
(f/g)′ = (f′g − fg′) / g².
What is the chain rule?
d/dx f(g(x)) = f′(g(x))·g′(x).
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?
sec² x.
What is the derivative of sec x?
sec x tan x.
What is the derivative of eˣ?
eˣ.
What is the derivative of ln x?
1/x, for x > 0.
What is the derivative of aˣ?
aˣ ln a.
What is the derivative of e^(3x)?
3e^(3x), by the chain rule.