Posted by **Tori** on Thursday, February 14, 2013 at 10:34pm.

Find the derivative of the function using the definition of a derivative.

F(x)=squareroot(1-3x)

Please show work for understanding, thank you! :)

- Calculus -
**Steve**, Friday, February 15, 2013 at 10:29am
recall that (a+b)^n = a^n + na^(n-1)*b + n(n-1)/2 a^(n-2)*b^2 + ...

So,

(1-3(x+h))^1/2 = ((1-3x) - 3h)^1/2

= (1-3x)^1/2 + (1/2)(1-3x^(-1/2)*(-3h) + (*)(-3h)^2 + ...

f(x+h) - f(x) =

(1-3x)^1/2 + (1/2)(1-3x^(-1/2)*(-3h) + (*)(-3h)^2 + ... - (1-3x)^1/2

= (1/2)(1-3x^(-1/2)*(-3h) + (*)(-3h)^2 + ...

now divide that by h to get

(1/2)(1-3x^(-1/2)*(-3) + (*)(9h) + ...

Now take the limit as h->0.

The (9h) term and all the other higher-power-of-h terms vanish, leaving

-3/2 (1-3x)^(-1/2)

## Answer this Question

## Related Questions

- calculus - Find the derivative of the function using the definition of ...
- Calculus - Use a symbolic differentiation utility to find the derivative of the ...
- Calculus derivatives - f(a) = a + √a (a) Find the derivative of the ...
- Calculus - Use derivative formulas to find the derivative of the function. ...
- calculus - Please help with this. I need the first derivative of f(x)=4(x+...
- calculus - You are given the following function. f(x)= (8+x)/(1-8x) (a) Find the...
- Calculus 1 - Could you please explain how to find the slope using the definition...
- Calculus - 1.) Find the derivative of tan (sec x). 2.) Find the derivative if 1/...
- Calculus - Find the derivative of m(x)=1/(x+1) by using the definition of the ...
- Calculus Help Please!!! - if f(x)= x+(1/x), find f'(x) using the limit ...

More Related Questions