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