Maths - Results Differentiation

 

type f(x) d f(x) / dx
constant a 0
power xn n*xn-1
exponential ex ex
trig functions sin(x) cos(x)
  cos(x) -sin(x)
  tan(x) sec2(x)
     
     
     
     
     
     
     
     
     
     
     
     
     
     

Derivation

Possibly the easiest way to derive these results is to convert the function into an infinite series, then differentiate the terms separately, then convert back to a function.

Alternatively we can often derive the results geometrically.

differentiation sin and cos

as we can see from the above construction, by congruent triangles:

d (sin θ) = dθ cos θ

and

d (cos θ) = - dθ sin θ

which gives:

d (sin θ)/dθ = cos θ

and

d (cos θ)/dθ = -sin θ

 

 

 

 

 

 

 

 

 


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