short finding derivative question?

Question

hi

i would like to find out how to solve this problem. i would like to find out

the derivative of
y = x5 multiplied by 5x or in notation x^5 . 5^x

thanks for your help. it is much appreciated.

Answer 1

Product rule, applying chain rule within

First function is x^5 and second function is 5^x
Product rule, need derivative of each
deriv of x^5 = 5x^4
deriv od 5^x = 5^x * ln5

5x^4 * 5^x + x^5 * 5^x ln5
simplifies to:
x^4 * 5^x (5 + x*ln5)

:)

Answer 2

i'm a little confused. You're asking for this derivative
y = (x^5)(5^x)?

If so, then by the Product Rule we have:
(x^5)(5^x ln 5) + (5^x)(5x^4)

You might need to simplify that some.

Answer 3

Don't look at it as:

x^5*5^x

Look at it like this:

u*v

You have to use the Product Rule, which states this:

(u')(v) + (u)(v')

Now we plug it in:

(5x^4)(5^x) + (x^5)(x5^(x - 1))

(5x^4)(5^x) + (x^6)(5^(x - 1))

And that's it.

Answer 4

y = x^5 . 5^x
<=> ln y = 5 ln x + x ln 5
<=> 1/y dy/dx = 5(1/x) + ln 5
<=> dy/dx = x^5.5^x (5/x + ln 5).

Answer 5

f(x) = a million/2x the guideline for spinoff of a quotient is d/dx u/v = ( v(du/dx) - u(dv/dx) )/ v^2 for this reason, u = a million, so it is less demanding d/dx (a million/v) = -(dv/dx) / v^2 v = 2x dv/dx = 2 d/dx (a million/2x) = -(2)/ (2x)^2 = -2/ (2x)^2 in case you have been to coach us your working, shall we element out the blunders.