CALC QUESTION: (Will medal)

An object moves along the x-axis with velocity of v(t) = t(sqrt(2t+3)) -3t

Find the acceleration of a(t) of the object.

I understand I need to find the derivative. But having issues

Question

CALC QUESTION: (Will medal)

An object moves along the x-axis with velocity of v(t) = t(sqrt(2t+3)) -3t

Find the acceleration of a(t) of the object.

I understand I need to find the derivative. But having issues

misty1212 · Answer

HI!!

anonymous · Answer

$$t \sqrt{2t+3} - 3t$$

misty1212 · Answer

HI!!you have a product, so you need the product rule for the first part

anonymous · Answer

Hi!

misty1212 · Answer

the derivative of $-3t$ is easy right? it is just $-3$

misty1212 · Answer

$$\left(fg\right).=f'g+g'f$$ with $$f(t)=t, f'(t)=1,g(t)=\sqrt{2t+3}, g'(t)=\frac{1}{\sqrt{2t+3}}$$

anonymous · Answer

Yes haha! Simple as that?

anonymous · Answer

Then will we have to use chain rule?

misty1212 · Answer

to find the derivative o f$\sqrt{2x+3}$ you use the chain rule (in your head)

misty1212 · Answer

the derivative of the square root of sommat is one over two square root of sommat, times the derivative of sommat
in this case the derivative of $2x+3$ is $2$ so the twos cancel

janu16 · Answer

hey misty do you think you can help me after youre done with this?

anonymous · Answer

Ah ok! Thank you for your time!

anonymous · Answer

Just confirming.... (sorry) @misty1212, I got the answer to be t - 3. Is that right?