Differential Calculus
Derivatives and differentiation expressions.
Differential calculus is a subfield of calculus that studies the rates at which quantities change.
Expression  Derivatives 

y = x^{n}  dy/dx = n x^{n1} 
y = a x^{n}  dy/dx = a n x^{n1} 
f(x) = a x^{n}  f'(x) = a n x^{n1} 
y = e^{x}  dy/dx = e^{x} 
y = e^{a x}  dy/dx = a e^{a x} 
y = a^{x}  dy/dx = a^{x} ln(a) 
y = ln(x)  dy/dx = 1 / x 
y = sin(Θ)  dy/dΘ = cos(Θ) 
y = cos(Θ)  dy/dΘ =  sin(Θ) 
y = tan(Θ)  dy/dΘ = sec^{2}(Θ) 
y = cot(Θ)  dy/dΘ = cosec^{2}(Θ) 
y = sec(Θ)  dy/dΘ = tan(Θ) sec(Θ) = sin(Θ) / cos^{2}(Θ) 
y = cosec(Θ)  dy/dΘ =  cot(Θ) cosec(Θ) =  cos(Θ) / sin^{2}(Θ) 
y = sin^{1}(x / a)  dy/dx = 1 / (a^{2}  x^{2})^{1/2} 
y = cos^{1}(x / a)  dy/dx =  1 / (a^{2}  x^{2})^{1/2} 
y = tan^{1}(x / a)  dy/dx = a / (a^{2} + x^{2}) 
y = cot^{1}(x / a)  dy/dx =  a / (a^{2} + x^{2}) 
y = sec^{1}(x / a)  dy/dx = a / (x (x^{2}  a^{2})^{1/2}) 
y = cosec^{1}(x / a)  dy/dx =  a / (x (x^{2}  a^{2})^{1/2}) 
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