Q. 3 G4.5( 4 Votes )
Differentiate the following from first principles
Answer :
We need to find derivative of f(x) = x2 ex
Derivative of a function f(x) is given by –
f’(x) = 
{where h is a very small positive number}
∴ derivative of f(x) = x2 ex is given as –
f’(x) = 
⇒ f’(x) = 
⇒ f’(x) = 
Using algebra of limits, we have –
⇒ f’(x) = 
⇒ 
As 2 of the terms will not take indeterminate form if we put value of h = 0, so obtained their limiting value as follows –
∴ f’(x) = 0×ex + 0 + 2x ex + 0 + 
Use the formula: 
⇒ f’(x) = 2x ex + x2 ex
⇒ f’(x) = 2x ex + x2 ex
Hence,
Derivative of f(x) = x2 ex = 2x ex + x2 ex
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