Differentiation | differentiation theory | Nda | IIT JEE | Agniveer

Differentiation

Common Standard formula

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Product rule

In this rule , we can differentiate two or more functions which are mulitplied together.

Example :
Find the derivative of y = xsinx

Video lecture :

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Divide rule / Quotient Rule

In this rule , we can differentiate two or more functions which are divided or in the rational fractional form ( in numerator and denominator form).

Example : Find the derivative of y = (xsinx)/(1+tanx)

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Chain Rule

In this rule , we can differentiate a function which is function of others function (e.g. Fog(x) or f(g(x))

Example :

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Differentiate w.r.t to another function

In this rule , we can differentiate a function f(x) with respect to another function g(x) not with respect to x.

Example : Find the derivative of the ln(x+sinx) with respect to (x+sinx).

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miscellaneous

Case 1 : if function is in form [f(x)]^g(x)
Example : y = sinx ^logx
take the log to the both the sides.
log y = log sinx ^logx
log y = logx . log sinx
differentiate w. r. t.
(1/y)dy/dx = (1/x) .logsinx + logx . (1/sinx) . cosx

Practice set 1 Practice set 2