Re: Differentiate a fraction

$\displaystyle x^2+2000*x^{-1}>>>>>2* x - 2000*x^{-2}$

Re: Differentiate a fraction

I would write the function as:

$\displaystyle f(x)=x^2+2000x^{-1}$

To differentiate, use the power rule term by term: $\displaystyle \frac{d}{dx}\left(kx^r \right)=krx^{r-1}$

Re: Differentiate a fraction

Re: Differentiate a fraction

What something such as $\displaystyle \frac{24300x-225x^3}{16}$

Surely since the 16^(-1) differentiates to 0, the whole equation differentiates to 0 (since everything is multiplied by 16^(-1))

Re: Differentiate a fraction

no ...

$\displaystyle \frac{d}{dx} \left[ c \cdot f(x)\right] = c \cdot f'(x)$

$\displaystyle y = \frac{1}{16}(24300x - 225x^3)$

$\displaystyle y' = \frac{1}{16}(24300 - 675x^2)$

fyi, problems involving derivatives belong in the calculus forum

Re: Differentiate a fraction

$\displaystyle f'(x)=\frac{1}{16} \left(24300-675 x^2\right)$

Re: Differentiate a fraction

Quote:

Originally Posted by

**skeeter** no ...

$\displaystyle \frac{d}{dx} \left[ c \cdot f(x)\right] = c \cdot f'(x)$

$\displaystyle y = \frac{1}{16}(24300x - 225x^3)$

$\displaystyle y' = \frac{1}{16}(24300 - 675x^2)$

fyi, problems involving derivatives belong in the calculus forum

Quote:

Originally Posted by

**MaxJasper** $\displaystyle f'(x)=\frac{1}{16} \left(24300-675 x^2\right)$

Wow I was always told to multiply out before doing any differentiating. Thanks for that!

Re: Differentiate a fraction

Can I do the same for integration? I.e. ignoring 15/16 until after I've integrated the thing in the brackets.

Re: Differentiate a fraction

$\displaystyle \int k \cdot f(x) \, dx = k \int f(x) \, dx$

look over your basic rules ... they're in your text.

Re: Differentiate a fraction

Quote:

Originally Posted by

**skeeter** $\displaystyle \int k \cdot f(x) \, dx = k \int f(x) \, dx$

look over your basic rules ... they're in your text.

You would be surprised.

How does one determine f(x)? Is it just anything involving an x? In other words, can I make anything k as long as it multiplies into the f(x) and does not involve x?

Re: Differentiate a fraction

k is a constant factor of the function