Question

find dy/dx given that y=x+5+3/√x

Answer 1

you may use the power rule for this

Answer 2

but first I would rewrite the term 3/(sqrt(x)

Answer 3

is the answer 1+3/2x^-3/2

Answer 4

I'll check just a sec :3

Answer 5

almost, there should be a negative before the first fraction

y=x+5+3x^(-1/2)
dy/dx = 1 - 3/2 x^(-3/2)

Answer 6

oh ok thanx can you just explain how it becomes a negative

Answer 7

sure.
it starts off as
\[\frac{ 3 }{ \sqrt{x} }\]but sqrt is the same thing as ^(1/2)
\[\frac{ 3 }{ x ^{1/2} }\]which is the same thing as....
\[3x ^{\frac{ -1 }{ 2 }}\]
so then when we apply the power rule, it becomes
\[(-\frac{ 1 }{ 2 }*3)x ^\frac{ -3 }{ 2 }\]
so the negative comes from the fact that the exponent on the x was negative

Answer 8

Thank you for your support Appreciate it :)

Answer 9

do you understand why
\[\frac{ 3 }{ x ^{\frac{ 1 }{ 2 }} } = 3x ^{\frac{ -1 }{ 2 }}\]
?

that's the only step I dont think I fully explained

Answer 10

Yes i do understand
Thank you
I'm an A level Student - just got mixed up with the signs
Thankyou loads!