Derivative AP Calculus Flashcards

What is the derivative of 𝑓(𝑥) = 𝑥^n with respect to 𝑥?

n * x^(n - 1)

What is the derivative of 𝑓(𝑥) = cos^(-1)(𝑥) with respect to 𝑥?

-1 / √(1 - x^2)

What is the derivative of 𝑓(𝑥) = arccot(𝑥) with respect to 𝑥?

-1 / (1 + x^2)

What is the derivative of 𝑓(𝑥) = a^𝑥 with respect to 𝑥?

a^x * ln(a)

What is the derivative of 𝑓(𝑥) = tan(𝑥) with respect to 𝑥?

sec^2(𝑥)

What is the derivative of 𝑓(𝑥) = cot(𝑥) with respect to 𝑥?

-csc^2(𝑥)

What is the derivative of 𝑓(𝑥) = csc(𝑥) with respect to 𝑥?

-csc(𝑥)cot(𝑥)

What is the derivative of 𝑓(𝑥) = sec(𝑥) with respect to 𝑥?

sec(𝑥)tan(𝑥)

What is the derivative of 𝑓(𝑥) = ln(𝑥) with respect to 𝑥?

1 / 𝑥

What is the derivative of 𝑓(𝑥) = 𝑦 with respect to 𝑥?

dy/dx (depends on y as a function of x)

What is the derivative of 𝑓(𝑥) = arctan(𝑥) with respect to 𝑥?

1 / (1 + x^2)

What is the derivative of 𝑓(𝑥) = sin(𝑥) with respect to 𝑥?

cos(𝑥)

What is the derivative of 𝑓(𝑥) = csc^(-1)(𝑥) with respect to 𝑥?

-1 / |x|√(x^2 - 1)

What is the derivative of 𝑓(𝑥) = arcsec(𝑥) with respect to 𝑥?

1 / |x|√(x^2 - 1)

What is the derivative of 𝑓(𝑥) = e^𝑥 with respect to 𝑥?

e^x

What is the derivative of 𝑓(𝑥) = cos(𝑥) with respect to 𝑥?

-sin(𝑥)

What is the derivative of 𝑓(𝑥) = log_b(𝑥) with respect to 𝑥?

1 / (x ln(b))

What is the derivative of 𝑓(𝑥) = arcsin(𝑥) with respect to 𝑥?

1 / √(1 - x^2)