HELP! C3 Differentiation question, Can't solve. Please help as soon as possible

Hi,

Guys the question is from differentiation chapter in C3.
I can solve the question but there is step i can't do in the question.

the question is

Question = X^3 x (2X + 6)^4

Answer : Let U= X^3 and V= (2X+6)^4

dU/dX= 2X^2 and dV/dX = 8(2X+6)^3.

You sure about dU/dx?

Yea im sure about dU/dX.

Why is that wrong?

You've calculated some sort of differential integral hybrid...

Multiply by the current power, then drop the power.

This is how its solved on solution bank.

I can't understand how they did the third last step.

Can u please explain that.

This is how its solved on solution bank.

I can't understand how they did the third last step.

Can u please explain that.

Hi there,

If the question is: y= x^3 (2x+6)^4

You have two different functions, x^3 (which is u) and (2x+6)^4 (which is v)

You've worked out du/dx and dv/dx

Because you have two different functions multiplied together you have to use the "product rule"

The product rule is: dy/dx = u.dv/dx + v.du/dx

Hence plug in the values that you've already calculated and you'll get an answer.

Let me know if you need any more help.

They took out a factor of $x^2(2x+6)^3$

They took out a factor of $x^2(2x+6)^3$

Yep, you're right. It took me a while but I've managed to explain the working here. Hopefully my workings out explain it a bit better!

Plug the values? Like how? Can you please explain more.

Yep, sure thing

You've already worked out how to get du/dx and how to get dv/dx

You also know what u and v both are.

You then use the values that you have for u, du/dx, v and dv/dx in the equation for the product rule. (Because it is two functions multiplied together, which we're calling u and v, we have to use the product rule.)

The product rule is: u dv/dx + v du/dx

Hence if you put the values of u, v, du/dx and dv/dx into the above equation, you'll get the first line of what was shown in the attachment you uploaded:

dy/dx = 8x^3 (2x+6)^3 + 3x^2 (2x+6)^4

If you then have a look at the workings out that I uploaded in my last post, you'll see how they get to an answer

Hope that helps - let me know if you need any more assistance

Yea i've already seen your attachment of the working you did. That was really helpful. Once again thank you very much.

No worries at all! Glad I could help you on this

If you need anything else just let me know