**Symbols used for derivative**

Contents

*dy/dx *or* f ‘(x) *or* D(y) *or *y’ *or y_{1 }*→ *First Order Derivative

*d ^{2}y/dx^{2}*

*or*

*f ”(x)*or

*D*or

^{2}(y)*y”*or y

_{2 }

_{ }

*→*Second Order Derivative

**Derivative of some standard Functions**

- d(x
^{n})/dx =nx^{n-1}n ∈ R; x>0^{ } - d(a
^{x})/dx =a^{x }ln a a>0 - d(e
^{x})/dx =e^{x} - d(ln x)/dx = 1/x

**Trigonometric Functions**

- d(sin
*x*)/dx = cos*x* - d(cos
*x*)/dx = -sin*x* - d(sec
*x*)/dx = sec*x*tan*x* - d(cosec
*x*)/dx = -cot*x*cosec*x* - d(tan
*x*)/dx =*sec*^{2 }*x* - d(cot
*x*)/dx =*–*cosec^{2 }*x*

**Inverse Trigonometric Functions**

- d(sin
^{-1}*x*)/dx = 1/(1-x^{2})^{1/2}-1< x <1^{ } - d(cos
^{-1}*x*)/dx = -1/(1-x^{2})^{1/2}-1< x <1^{ } - d(cot
^{-1}*x*)/dx = -1/(1+x^{2}) x∈ R - d(tan
^{-1}*x*)/dx = 1/(1+x^{2}) x∈ R - d(sec
^{-1}*x*)/dx = 1/|x|(x^{2}-1)^{1/2 }|x|>1 - d(cosec
^{-1}*x*)/dx = -1/|x|(x^{2}-1)^{1/2 }|x|>1

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