Question

Help Calc!

Answer 1

\[ w = \sqrt{(x ^{2} * 5^{x}})^{3}\]

Answer 2

so there are

w=sqrt(x^2 *5^x)^3
yes ?

Answer 3

so this you need to si,plifie it ?

Answer 4

simplifie it ?

Answer 5

so i think will help you if you know how you can writing the squarroot using exponent

do you know it ?

Answer 6

i need to use chain rule to find the derivative of the function

Answer 7

\[w=\sqrt{(x^2*5^x)^3}=[(x^2*5^x)^{3}]^{1/2}=(x^2*5^x)^{3/2}\]
It might help you to differentiate it easier if you rewrite the square root as a fractional exponent.
From here you'll take the derivative starting from the outermost function, applying the power rule to that exponent.

Answer 8

well the answer is \[3/2x ^{2}\sqrt{5^{3x}}(2+x \ln 5)\]

Answer 9

I am stuck on w'(x) = \[1/2(x ^{2}*5^{x})^{3} * 3 (x ^{2} *5^{x})^{2} * 2x (\ln5) 5^{x}\]

Answer 10

you really should combine those powers before you apply the derivative, don't do the square root THEN the cube .. change it a 3/2 power.

Also, part of the trouble you're running into is, you're forgetting that the INNER function is the product of 2 terms involving x. So you'll need to apply the product rule for that inside part! <:D

Answer 11

can you break it down for me :/

Answer 12

Ok this is where we want to start, we want to simplify it nice n pretty like this before we attempt to take a derivative.