Differentiation All Formula Class 12
d/dx (sin x)= cosx [where x is angle (θ)]
d/dx (cos x)= -sinx
d/dx (tan x)= sec²x
d/dx (cot x)= -cosec²x
d/dx (sec x)= secx.tanx
d/dx (cosec x)= -cosecx.cotx
d/dx (constant)= 0 (Zero)
d/dx (logx)= 1/x
d/dx (a^x) = a^x/loga
d/dx (e^x)= e^x [exponential function]
d/dx (e^-x)= -e^x
d/dx (x)= 1
d/dx (y)= dy/dx [with respect to x.]
Differentiation For Inverse Function
d/dx (sin–1x) = 1/√(1-x2)
d/dx (cos–1x) = -1/√(1-x2)
d/dx (tan–1x) = 1/(1+x2)
d/dx (cot–1x) = -1/(1+x2)
d/dx (sec–1x) = 1/[x.√(x2 – 1)]
d/dx (cosec–1x) = -1/[x.√(x2 – 1)]
Differentiation For Product Rule
d/dx (U×V) = U.d/dx (V)+V.d/dx (U)
Example:- x.sinx
solution:-
Let, y=x.sinx [here x is ‘U’ & sinx is ‘V’]
dy/dx= x.d/dx(sinx)+sinx.d/dx(x)
dy/dx= x.cosx+sinx
Ans- dy/dx= x.cosx+sinx