Question

y=x^3×3√x
Please find its derivative

Answer 1

with respect to what variable

Answer 2

Y

Answer 3

dy/dx?

Answer 4

Yes

Answer 5

dy/dx

Answer 6

first you need to use power rule
\[x^n = n(x ^{n-1})\]

Answer 7

also you need to use product rule, because you are multiplying 2 functions with a variable (x) term

Answer 8

You can see the question here

Answer 9

yes I am helping you...

Answer 10

I appreciate that kindly do solve it for me please thank you

Answer 11

I am helping you solve it, not solving it for you.

Answer 12

do you know power rule?

Answer 13

Yes

Answer 14

\[\sqrt[3]{x}=x ^{1/3}\]
You know power rule, I just told you that.
Do you know product rule? (last rule you need to know for this problem)

Answer 15

\[f(x)\times g(x)= f(x) \times g'(x)+g(x) \times f'(x)\]
just in case you don't know this is product rule

Answer 16

lets treat x^3 as f(x)
and x^(1/3) as another function
now we need to apply power rule to both to find the derivatives (of each individually), then apply product rule to find the derivative

Answer 17

\(\color{#0cbb34}{\text{Originally Posted by}}\) darkknight
first you need to use power rule
\[x^n = n(x ^{n-1})\]
\(\color{#0cbb34}{\text{End of Quote}}\)
following this, x^3 = 3x^(3-1) = 3x^2
correct?

Answer 18

sorry x^3 doesn't equal 3x^2, 3x^2 is the derivative of x^3 (fyi)

Answer 19

applying the same logic, x^(1/3)
the derivative is (1/3)(x)^(1/3-1) = \[1/3x ^{-2/3}\]

Answer 20

now you know \[f(x), f'(x), g(x), g'(x)\]
apply product rule

Answer 21

Thank You

Answer 22

np : ) have a good day~

Answer 23

Found the answer

Answer 24

\(\color{#0cbb34}{\text{Originally Posted by}}\) darkknight
\[f(x)\times g(x)= f(x) \times g'(x)+g(x) \times f'(x)\]
just in case you don't know this is product rule
\(\color{#0cbb34}{\text{End of Quote}}\)
f(x) = x^3, f'(x) = 3x^2, g(x) = x^(1/3), g'(x) = 1/3)(x)^(-2/3)
If you plug all of these into product rule formula you should get the correct answer