OpenStudy (anonymous):

find dy/dx given that y=x+5+3/√x

3 years ago
OpenStudy (anonymous):

you may use the power rule for this

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

I'll check just a sec :3

3 years ago
OpenStudy (anonymous):

almost, there should be a negative before the first fraction y=x+5+3x^(-1/2) dy/dx = 1 - 3/2 x^(-3/2)

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

Thank you for your support Appreciate it :)

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

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

3 years ago
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