## IB Maths SL,Calculus Quotient Rule

Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths SL Revision Notes

### IB Maths SL,Calculus Quotient Rule

IB Mathematics SL – Calculus, Derivatives, Differentiation Quotient Rule

How can we find the first derivative function of $h(x)=\frac{x^2}{e^x}$ ??

Thanks
Oliver

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Joined: Mon Jan 28, 2013 8:08 pm

### Re: IB Maths SL,Calculus Quotient Rule

IB Mathematics SL – Derivatives, Differentiation Quotient Rule

We know that the derivative of the quotient of two functions is given by the following formula

$(\frac{f(x)}{g(x)})'=\frac{f'(x)g(x)-f(x)g'(x)}{g^2 (x)}$

So about your question we notice that $h(x)$ can be treated as a quotient of two functions $x^2 \and\ e^x$ .

Using the quotient rule we obtain

$(\frac{x^2}{e^x})'=\frac{( x^2)'(e^x)+ ( x^2) ( e^x)'}{(e^x)^2}=$

$=\frac{2x e^x + x^2 e^x}{e^{2x}}=$

$=\frac{ e^x (2x + x^2 )}{e^{2x}}=$

$=\frac{2x + x^2 }{e^x}$

Hope these help!!
miranda

Posts: 268
Joined: Mon Jan 28, 2013 8:03 pm

### Re: IB Maths SL,Calculus Quotient Rule

thanks!!
Oliver

Posts: 0
Joined: Mon Jan 28, 2013 8:08 pm