Question

Calculate dy/dx. Simplify your answer.
y = x^5√x

Answer 1

I know I use the power rule, after multiplying it out. But the square root is confusing me.

Answer 2

\[x ^{5}\sqrt{x}=x^{5+1/2}=x^{5.5}\]

Answer 3

Hence
\[dx/dy= 5.5x^{4.5}=5.5x^4\sqrt{x}\]

Answer 4

I assume you know
\[\sqrt{x}=x^{1/2}\]

Answer 5

so you just multiplied x^5 and x^1/2. And then used the power rule, right? O_O

Answer 6

Yes I knew that. x3

Answer 7

Exactly

Answer 8

Ohhhh okay, I see I see. That square root was tripping me up so badly. thank you very much for your help.

Answer 9

you would use the product rule because it's technically (x^5)(x^1/2)

Answer 10

either way.