Derivative help please! w=(t^5+3)^52
Find dw/dt

Question

Derivative help please! w=(t^5+3)^52
Find dw/dt

sweetburger · Answer

Got to use the chain rule here.

xguardians · Answer

@awesomness82, do you know the chain rule?

anonymous · Answer

I do but I am a little confused because there is no w equation. I tried finding the derivative of dt (for which I got 260x^49x^5+3)^51) and multiplying that by the original equation but I didn't get the right answer

nnesha · Answer

the inside function would stay the same when u take the derivative of outer function 
$$(x^3)^4$$
 the derivative would be $$4(x^3)^3  \cdot 3x^2$$

nnesha · Answer

ohh wait i see what u did there

nnesha · Answer

you can't distribute  52(t^5+3)^{51} by 5t

nnesha · Answer

how did you get x^{49} ??

xguardians · Answer

Derivative would be 52 * (5t^4) * (t^5 + 3)^51

xguardians · Answer

You pull down the 52, and subtract one from the exponent. Then you take the derivative of the inside, which is simply 5t^4 and multiply everything by that, granting you the equation above.

xguardians · Answer

Which should be simplified:
$$260t^4(t^5+3)^{51}$$

anonymous · Answer

Oh okay thank you! I didn't realize I had to subtract from the exponent to make it 51

xguardians · Answer

The chain rule had me confused for the longest time, best of luck with your studies :)