Standard Derivatives Flashcards
What is the derivative of xⁿ?
d/dx [ xⁿ ] ⇒ n·xⁿ⁻¹
What is the derivative of √x?
d/dx [ √x ] = d/dx[x^(1/2)] ⇒ (1/2)x^(–1/2)
What is the derivative of eˣ?
d/dx [ eˣ ] ⇒ eˣ
What is the derivative of aˣ?
d/dx [ aˣ ] ⇒ aˣ·ln(a)
What is the derivative of ln(x)?
d/dx [ ln(x) ] ⇒ 1/x
What is the derivative of logₐ(x)?
d/dx [ logₐ(x) ] ⇒ 1/(x·ln(a))
What is the derivative of sin(x)?
d/dx [ sin(x) ] ⇒ cos(x)
What is the derivative of cos(x)?
d/dx [ cos(x) ] ⇒ –sin(x)
What is the derivative of tan(x)?
d/dx [ tan(x) ] ⇒ sec²(x)
What is the derivative of cot(x)?
d/dx [ cot(x) ] ⇒ –csc²(x)
What is the derivative of sec(x)?
d/dx [ sec(x) ] ⇒ sec(x)·tan(x)
What is the derivative of csc(x)?
d/dx [ csc(x) ] ⇒ –csc(x)·cot(x)
What is the derivative of arcsin(x)?
d/dx [ arcsin(x) ] ⇒ 1/√(1–x²)
What is the derivative of arccos(x)?
d/dx [ arccos(x) ] ⇒ –1/√(1–x²)
What is the derivative of arctan(x)?
d/dx [ arctan(x) ] ⇒ 1/(1+x²)
What is the derivative of arccot(x)?
d/dx [ arccot(x) ] ⇒ –1/(1+x²)
What is the derivative of arcsec(x)?
d/dx [ arcsec(x) ] ⇒ 1/(|x|·√(x²–1))
What is the derivative of arccsc(x)?
d/dx [ arccsc(x) ] ⇒ –1/(|x|·√(x²–1))
What is the derivative of f(x) + g(x)?
d/dx [ f(x) + g(x) ] ⇒ f′(x) + g′(x)
What is the derivative of c·f(x)?
d/dx [ c·f(x) ] ⇒ c·f′(x)
What is the product rule for derivatives?
d/dx [ f(x)·g(x) ] ⇒ f′(x)·g(x) + f(x)·g′(x)
What is the quotient rule for derivatives?
d/dx [ f(x)/g(x) ] ⇒ [f′(x)·g(x) – f(x)·g′(x)] / [g(x)]²
What is the chain rule for derivatives?
d/dx [ f(g(x)) ] ⇒ f′(g(x))·g′(x)
What is the derivative of y with respect to x in parametric form?
Parametric: dy/dx ⇒ (dy/dt) / (dx/dt)
