# Math Help - Differentiation? Equation of the tangent line?

1. ## Differentiation? Equation of the tangent line?

I'm new to Calculus and am having a hard time adjusting to the new environment of University! Thanks all for looking.

f(x) = 4pi^4

f'(x) = ?

--------------------------------------------------

Find an equation of the tangent line to the curve at the given point.
(Assume the tangent line form to be f(x) = mx + b.)

y=e^x/x (1, e)

m= ?
b= ?

----------------------------------------------------

Find f '(x) and f ''(x). f(x) = x^9e^x

f'(x) = ?
f''(x) = ?

Thanks again. These are the problems I left for last and I have no idea how to solve them.

2. Originally Posted by akifbayram
I'm new to Calculus and am having a hard time adjusting to the new environment of University! Thanks all for looking.

f(x) = 4pi^4

f'(x) = ?

what is the derivative of a constant?

--------------------------------------------------

Find an equation of the tangent line to the curve at the given point.
(Assume the tangent line form to be f(x) = mx + b.)

y=e^x/x (1, e)

find y'(x) and evaluate y'(1) to get the slope of the tangent line.

----------------------------------------------------

Find f '(x) and f ''(x). f(x) = x^9e^x

use the product rule to find f'(x) ... you'll have to use it again to find f''(x)

f'(x) = ?
f''(x) = ?
...

3. 1. 0 ?

2. Working on that...

3. f'(x) = (9x^8)(e^x) + (x^9)(xe^(x-1))
= e^(x-1) x^8 (x^2+9 e)

f''(x)= Working on this too..

4. Originally Posted by akifbayram
1. 0 ? yes

2. Working on that...

3. f'(x) = (9x^8)(e^x) + (x^9)(xe^(x-1)) no ... what is the derivative of e^x?
...

5. Derivative of e^x is itself?

so it would be...
f'(x)=(9x^8)(e^x)+(x^9)(e^x))
f'(x)=(e^x) (x^8) (x+9)
f''(x)=e^x(8x^7)+e^x(x^8)*(x+9)+(e^x)(x^8)(1)
f''(x)=(e^x)(x^9+10)(e^x)(x^8+8)(e^x)(x^7)

6. $f(x) = x^9 e^x$

$f'(x) = x^9 e^x + 9x^8 e^x$

$f'(x) = e^x(x^9 + 9x^8)$

$f''(x) = e^x(9x^8 + 72x^7) + e^x(x^9 + 9x^8)$

$f''(x) = e^x[(9x^8 + 72x^7) + (x^9 + 9x^8)]$

$f''(x) = e^x(x^9 + 18x^8 + 72x^7)$

$f''(x) = x^7 e^x(x^2 + 18x + 72)$