differentiation using trigonometric substitution


differentiation using trigonometric substitution

differentiate. arctan √ [(1-x)/(1+x)] w.r.t.x

here the direct differentiation will be complicated involving inverse trigonometric function
square root , quotient rule etc.
therefore use the substitution x = tan(theta), simplify and then differentiate

                arctan √ [(1-x)/(1+x)] w.r.t.x using trigonometric



find the derivative of f(x) =1/x at x=3 using the lim {f(x)-f(a)} / {x-a} as x---->a

derivative of f(x)
                =1/x at x=3 using the lim {f(x)-f(a)} / {x-a} as

here you first find f(x)-f(3) simplify it , then divide with(x-3)
cancel off the common factors and then apply limit as x--> 3


if √(xy) = x - 2y, find dy/dx using implicit differentiation

if √(xy) = x - 2y,
                find dy/dx using implicit differentiation

when differentiating the given expression w.r.t x  use function of function rule
for √ and then product rule for (xy) and do not forget to use dy/dx as the
derivative of y.

other questions and problems:

*integral calculus integration formula

trigonometric identity and ratio of  certain standard angles

*list of differentiation formula     *integral calculus integration formula
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