Rules of Differentiation flashcards

13

from “The Derivative As a Limit”

9

from “The Derivative As a Limit”

$\frac{d^{2}y}{d{x}^2}$d²y/dx²

from “Derivative Notation”

f'(x)

from “Derivative Notation”

$3x^2$3x²

from “Differentiating From First Principles”

2x

from “Differentiating From First Principles”

yes

from “Where a Derivative Fails to Exist”

no

from “Where a Derivative Fails to Exist”

9

from “Differentiating Linear Functions”

4

from “Differentiating Linear Functions”

12x

from “The Power Rule”

$\frac{1}{\left(2\sqrt{x}\right)}$1/(2√x)

from “The Power Rule”

12x + 6

from “The Constant Multiple and Sum Rules”

8x + 2

from “The Constant Multiple and Sum Rules”

$4x^3$4x³

from “The Product Rule”

$3x^2$3x²

from “The Product Rule”

$v^2$v²

from “The Quotient Rule”

u'v − uv'

from “The Quotient Rule”

3 cos(3x)

from “The Chain Rule”

$9{\left(3x+1\right)}^2$9(3x + 1)^2

from “The Chain Rule”

−cos x

from “Differentiating Trigonometric Functions”

cos x

from “Differentiating Trigonometric Functions”

$-{\mathrm{cosec}}^{2}x$−cosec²x

from “Differentiating tan x and the Reciprocal Ratios”

−cosec x cot x

from “Differentiating tan x and the Reciprocal Ratios”

its own height

from “The Number E”

$e^x$eˣ

from “The Number E”

$\frac{1}{x}$1/x

from “Differentiating Exponentials and Logarithms”

$e^x$eˣ

from “Differentiating Exponentials and Logarithms”

$\frac{1}{\left(x\ln 2\right)}$1/(x ln 2)

from “Differentiating aˣ and logₐ x”

$5^x\ln 5$5ˣ ln 5

from “Differentiating aˣ and logₐ x”

$-3x/y$−3x / y

from “Implicit Differentiation”

$-4x/y$−4x / y

from “Implicit Differentiation”

f(a) = b

from “The Derivative of an Inverse Function”

$f\left(f^{-1}\left(x\right)\right)=x$f(f⁻¹(x)) = x

from “The Derivative of an Inverse Function”

$\frac{1}{\left(1+x^2\right)}$1/(1 + x²)

from “Differentiating sin⁻¹ x and tan⁻¹ x”

$1+x^2$1 + x²

from “Differentiating sin⁻¹ x and tan⁻¹ x”

12x

from “Higher Derivatives”

30x

from “Higher Derivatives”