Derivative Formulas and Hyperbolic Trigonometric Functions

These flashcards cover key concepts related to derivative formulas and hyperbolic trigonometric functions.

derivative of sin(x)

cos(x), which is the rate of change of the sine function.

derivative of cos(x)

-sin(x), which shows the negative rate of change of the cosine function.

Derivative of tangent function (tan)

sec²x

Cos and sin identity

Sin²x + cos²x = 1

Hyperbolic sin and cos identity

Cosh²x - sinh²x = 1

Derivative of cosecant function (csc)

-cscxcotx

Derivative of sec

Secxtanx

Derivative of cot

-csc²x

hyperbolic sine (sinh)

A hyperbolic function defined as (e^x - e^-x)/2.

Derivative of b^f(x)

b^f(x)lnb times f’(x)

Derivative of logbf(x)

1/f(x)lnb times f’(x)

hyperbolic cosine (cosh)

A hyperbolic function defined as (e^x + e^-x)/2.

derivative of sinh(x)

cosh(x)

derivative of cosh(x)

sinh(x)

inverse hyperbolic sine derivative

1/(1+x²)^1/2

Inverse hyperbolic cos derivative

1/(x² - 1)^1/2

Inverse hyperbolic tan derivative

1/(1-x²)

derivative of tanh(x)

sech^2(x)

Derivative of inverse sin

1/(1-x²)^1/2

Derivative of inverse cos

-1/(1-x²)^1/2

Derivative of inverse csc

-1/x(x²-1)^1/2

Derivative of inverse sec

1/x(x²-1)^1/2

Derivative of inverse tan

1/x²+1

Derivative of inverse cot

-1/x²+1