Let f(x) = sinx then,
Let f(x) = secx
Let then x = siny.
Differentiating w.r.t x we get,
Let y = sec-1x then secy = x.
Differentiating w.r.t x we have,
Why and not ?
Note that y = sec-1x is an increasing function in its domain.
Different Methods of Differentiation:
1) Differentiation of a function defined parametrically:
Let x, y be function of parameter t, i.e.
x = f (t), y = f (t) then,
2) Logarithmic Differentiation:
The process of taking logarithm on both sides and then differentiating is called logarithmic differentiation.
Differentiate w.r.t x.
Let y = .
Taking logarithm on both sides, then we have
logy = sinx.logx
3) Differentiation of Implicit function:
If the relation between x and y is given by equation containing both and this equation is not immediately solvable for y, then y is called implicit function of x.
If Then prove that
Given that differentiating on both sides w.r.t x we have,