Question

if h(x)=sqrt(2+2f(x)) where f(1)=7 and f'(1)=2 find h'(1)

Answer 1

@Psymon

Answer 2

@Hero

Answer 3

@aaronq @Directrix

Answer 4

can you find the derivative of
\[ \sqrt{2+2f(x)} \]
?

Answer 5

no

Answer 6

do you know the power rule for taking the derivative of \( x^n\) ?
\[ d x^n = n x^{n-1} dx \]

re-write the square root as
\[ (2+2f(x))^{\frac{1}{2}} \]
and use the power rule

Answer 7

yeah the power rule is nx^(n-1)

Answer 8

the power rule works even if n is a fraction. anything to the 1/2 power is the same as the square root

Answer 9

ok so it would be (sqrt(2+2f(x)))/2

Answer 10

\[ (2+2f(x))^{\frac{1}{2}} \]

the rule says "bring down" the 1/2 so you will get times 1/2
then make a new exponent = 1/2 - 1
you did not do that part

Answer 11

ok it would be -(sqrt(2+2f(x)))/2

Answer 12

first, get rid of the square root. use to the 1/2 power instead
\[ (2+2f(x))^{\frac{1}{2}} \]

now apply the rule
\[ d x^n = n\ x^{n-1} dx \]
in your case, n = 1/2 and x is (2 + 2 f(x) )

Answer 13

ok i am lost. what would it be then

Answer 14

Are you asking how to interpret the power rule ?
\[ d x^n = n\ x^{n-1} dx \]
says, to take the derivative of x^n write n out front.
then find n-1, and write \( x^{n-1}\)
then take the derivative of x

try those steps on
\[ (2+2f(x))^{\frac{1}{2}}\]

Answer 15

\[(1/2)(2+2f(x))^{-1/2}\]

Answer 16

yes, but the last step is take the derivative of x, or in this case
\[ d ( 2 + 2 f(x) ) \]

Answer 17

d(2 + 2 f(x)) = d(2) + d (2 f(x) )

derivative of a constant 2 is 0.
d (2 f(x)) is 2 * d (f(x))
we don't know the details of f(x) so that is the answer: d (f(x))
d( f(x) ) is also written f'(x)
(it means the same thing)

Answer 18

so you now have
\[ \frac{1}{2}(2+2f(x))^{-1/2} 2 f'(x) \]
which you can simplify to
\[ (2+2f(x))^{-1/2} f'(x) \]
or if you don't like negative exponents, you can "flip" it and wriate
\[ \frac{f'(x)}{(2+2f(x))^{\frac{1}{2}}}\]
or if you would rather see the square root instead of the 1/2 power
\[ \frac{f'(x)}{\sqrt{2+2f(x)}} \]

Answer 19

now you can find the answer
using f(1)=7 and f'(1)=2 find h'(1)

Answer 20

so its 2/sqrt30

Answer 21

you have
\[ h'(x) = \frac{f'(x)}{\sqrt{2+2f(x)}} \]

you know f(1) =7 and f'(1)=2
so you can find h'(1)

Answer 22

i got 2/sqrt30

Answer 23

what is 2+ 2*7

Answer 24

never mind its 2/sqrt16=1/2

Answer 25

much better.