# Thread: find the gradient at the following points at the given (part2)

1. ## find the gradient at the following points at the given (part2)

hi,
i don't understand how i would find the gradient at the following points at the given points:
y=3/x+2x+1 x=7

i know i would do:
y=3x^-1+2x+1
dy/dx=-3x^-2+2

im stuck after this because is i substitute it it looks like this:
dy/dx=-21^-2+2

what would i do from here??

thanks!

2. ## Re: find the gradient at the following points at the given (part2)

Is $\displaystyle y=\frac{3}{x+2x+1}$ or $\displaystyle y=\frac{3}{x}+2x+1$ ?

3. ## Re: find the gradient at the following points at the given (part2)

the second one, soory for the confusion!

4. ## Re: find the gradient at the following points at the given (part2)

Originally Posted by andyboy179
hi,
i don't understand how i would find the gradient at the following points at the given points:
y=3/x+2x+1 x=7

i know i would do:
y=3x^-1+2x+1
dy/dx=-3x^-2+2
Correct

im stuck after this because is i substitute it it looks like this:
dy/dx=-21^-2+2

what would i do from here??

thanks!
That's an incorrect substitution: $\displaystyle -3x^{-2} +2 = -\dfrac{3}{x^2} + 2$. You appear to have included -3 in the exponent which is not the case.

5. ## Re: find the gradient at the following points at the given (part2)

i tought i have to sub 7 into it so i did -3^-2x7= -21^-2. if the top part is correct how would i find the gradient?

6. ## Re: find the gradient at the following points at the given (part2)

Originally Posted by andyboy179
i tought i have to sub 7 into it so i did -3^-2x7= -21^-2. if the top part is correct how would i find the gradient?
-3 is not squared, only the 7 is squared. What you want to do is $\displaystyle -3 \times \left(7^{-2}\right)$

7. ## Re: find the gradient at the following points at the given (part2)

oh, so it would be 7^2= 49 then dy/dx=-3/49+2?

Correct!

10. ## Re: find the gradient at the following points at the given (part2)

Originally Posted by andyboy179
Yes although since they are both numbers you should combine like terms to simplify your answer. I suggest writing $\displaystyle 2 = \dfrac{98}{49}$ and get $\displaystyle \dfrac{-3}{49} + \dfrac{98}{49} = \dfrac{95}{49}$