Question

Calculate the second and third derivatives of
y = 5x − 4/(x) I know you use the quotient rule, but I just need to check my work

Answer 1

Use Wolfram Alpha to check your work. Type: 'differentiate y=5x-4/x'. http://www.wolframalpha.com/

Answer 2

This is actually exactly like the last one you did (z-4/z), they're just using a different variable instead of z and they added a coefficient (5). You can just use the power rule for this.

Answer 3

Unless you meant to write y = (5x-4)/x

Answer 4

If that's the case, you could still use just the power rule by breaking up the fraction:\[y = \frac{5x-4}{x} = \frac{5x}{x}-\frac{4}{x} = 5 - \frac{4}{x}\]

Answer 5

ohhh, wow that is the same thing, just written differently

Answer 6

-4/x = -4x^-1?

Answer 7

Yes

Answer 8

cool

Answer 9

what if its just a number over the top, like 2/ (x-2)

Answer 10

or 4/ (2 + x)

Answer 11

You could also use the power rule. (Actually, I knew a professor who had never heard of the quotient rule; it can always be done with the power rule instead)\[4(2+x)^{-1}\]

Answer 12

so 2^-1 + x^-1 ... then 8^-1 + 4x^-1....... -4x^-2,8x^-3, -24x^-4?

Answer 13

No, it wouldn't be 2^-1+x^-1:\[\frac{d}{dx}(4(x+2)^{-1}) = (-1)(4)(x+2)^{-2} = \frac{-4}{(x+2)^{2}}\]

Answer 14

Remember:\[\frac{1}{a} + \frac{1}{b} \neq \frac{1}{a+b}\]

Answer 15

so the next one will be -4 (-2) / x+2^4

Answer 16

No, the exponent is reduced by 1, not 2. Also, the way you have it typed, the ^4 would only effect the 2; you would need x+2 kept in the parentheses. So the 2nd derivative would be:\[\frac{(-4)(-2)}{(x+2)^{-3}} = \frac{8}{(x+2)^{3}}\]

Answer 17

dang i missed it by an exponent

Answer 18

sorry, that -3 exponent shouldn't be negative

Answer 19

what if it has an e in it?

Answer 20

a variable and an e?

Answer 21

Well all the same rules apply, you just have to remember that e is a number/constant. It's easy to forget, but remember:\[\frac{d}{dx}e = 0\]

Answer 22

so would sqrt w * e^w be e *2w^-1/2