Symbolab Derivatives Cheat Sheet

Symbolab Derivatives Cheat Sheet

Derivative Rules:

Power Rule: () = -1

Derivative of a Constant: () = 0

Sum/Difference Rule:

( ? ) = ?

Constant Out: ( ) =

Product Rule:

( ) = +

Quotient Rule:

()

=

- 2

Chain Rule: () =

Common Derivatives:

(ln()) = 1

(ln(||)) = 1

() =

Trigonometric Derivatives:

(sin()) = cos()

(cos()) = - sin()

(tan()) = sec2()

(log())

=

1 ln(10)

(log())

=

1 ln()

(sec())

=

tan() cos()

(csc())

=

- cot() sin()

(cot())

=

-

1 sin2()

Arc Trigonometric Derivatives:

(arcsin())

=

1 1-2

(arccos())

=

-

1 1-2

(arctan())

=

1 2+1

(arcsec())

=

1 2(2-1)

(arccsc())

=

-

1 ||2-1

(arccot())

=

-

1 2+1

Hyperbolic Derivatives:

(sinh()) = cosh()

(cosh()) = sinh()

(tanh()) = sech2()

(sech()) = - sech() tanh()

 (csch()) = - coth() csch()

(coth()) = - csch2()

Arc Hyperbolic Derivatives:

(arcsinh())

=

1 2+1

(arccosh()) = 1

-1+1

(arcsech())

=

+2 1-1 (-1)

(arctanh())

=

1 1-2

(arccsch()) = - 1

212+1

(arccoth())

=

1 1-2

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