≥Better Grades
Menu
Formula sheet · Calculus I · Unit 2A

Derivative Rules Formula Sheet and Printable PDF

A compact, readable reference for core derivative rules with rule-selection cues and examples.

Reference format15 min estimated timeReference progression

What is included

Review power, product, quotient, chain, exponential, logarithmic, trigonometric, and inverse-trigonometric derivative rules.

Skills assessed

  • selecting derivative rules
  • differentiating standard functions

Prerequisites

  • function notation
  • algebra
Derivative Rules Formula Sheet instructional sequence
A compact, readable reference for core derivative rules with rule-selection cues and examples. The numbered labels and written sequence preserve meaning without relying on color.
Long description

Read the diagram from top to bottom. Each numbered box names one decision or mathematical operation. Arrows show the required order; the text labels remain the complete interpretation in print, dark mode, and nonvisual reading.

Printable and accessible

Download this resource

No email address or account is required.

Student PDF (opens in a new tab)SVGPNG

Reference formulas

Linearity

(c)′=0(c)'=0(xn)′=nxn−1(x^n)'=nx^{n-1}(f±g)′=f′±g′(f\pm g)'=f'\pm g'

Products and quotients

(fg)′=f′g+fg′(fg)'=f'g+fg'(f/g)′=(f′g−fg′)/g2(f/g)'=(f'g-fg')/g^2

Composition

(f∘g)′=f′(g(x))g′(x)(f\circ g)'=f'(g(x))g'(x)

Exponential and logarithmic

(ex)′=ex(e^x)'=e^x(ax)′=axln⁡a(a^x)'=a^x\ln a(ln⁡x)′=1/x(\ln x)'=1/x

Trigonometric

(sin⁡x)′=cos⁡x(\sin x)'=\cos x(cos⁡x)′=−sin⁡x(\cos x)'=-\sin x(tan⁡x)′=sec⁡2x(\tan x)'=\sec^2x

Inverse trigonometric

(arcsin⁡x)′=1/1−x2(\arcsin x)'=1/\sqrt{1-x^2}(arctan⁡x)′=1/(1+x2)(\arctan x)'=1/(1+x^2)

Common errors

  • Multiplying derivatives in a product.
  • Reversing quotient-rule numerator order.
  • Forgetting the inner derivative in a composition.

Learn fully

Supporting steps