Derivatives and Differentiation Rules

Flashcards covering basic derivative formulas for trigonometric, inverse trigonometric, exponential, and logarithmic functions, as well as the Power, Product, Quotient, and Chain rules of differentiation.

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 sin⁻¹ x?

\frac{1}{\sqrt{1-x^2}}

What is the derivative of cos⁻¹ x?

-\frac{1}{\sqrt{1-x^2}}

What is the derivative of tan⁻¹ x?

\frac{1}{x^2+1}

What is the derivative of cot⁻¹ x?

-\frac{1}{x^2+1}

What is the derivative of sec⁻¹ x?

\frac{1}{|x|\sqrt{x^2-1}}

What is the derivative of csc⁻¹ x?

-\frac{1}{|x|\sqrt{x^2-1}}

What is the derivative of eˣ?

e^x

What is the derivative of aˣ?

a^x \ln a

What is the derivative of ln x?

\frac{1}{x}

What is the derivative of log x?

\frac{1}{x \ln b}

State the Power Rule for derivatives.

\frac{d}{dx} (x^n) = n x^{n-1}

State the Product Rule for derivatives.

\frac{d}{dx} (uv) = u'v + uv'

State the Quotient Rule for derivatives.

\frac{d}{dx} \left(\frac{u}{v}\right) = \frac{u'v - uv'}{v^2}

State the Chain Rule for derivatives.

\frac{d}{dx} (f(g(x))) = f'(g(x))g'(x)