# Calculus I level question, find the derivative?

• Oct 19th 2008, 09:07 AM
akarouette
Calculus I level question, find the derivative?
Given: r(2)=4, s(2)=1, r'(2)=-1, s'(2)=3, s'(4)=3, find the derivatives or state what information you would need to find them for:
H'(2) if H(x)=r(x)s(x)
H'(2) if H(x)=square root of r(x)
H'(2) if H(x)=r(s(x))
H'(2) if H(x)=s(r(x))

• Oct 19th 2008, 10:29 AM
Shyam
1).H(x) = r(x)s(x)

differentiate, using product rule,

H'(x) = r(x)s'(x) + r'(x)s(x)

H'(2) = r(2)s'(2) + r'(2)s(2)

H'(2) =(4)(3) + (-1)(1) = 11

2).

$\displaystyle H(x) = \sqrt{r(x)}$

differentiate,

$\displaystyle H'(x) = \frac{1}{2\sqrt{r(x)}}r'(x)$

$\displaystyle H'(2) = \frac{1}{2\sqrt{r(2)}}r'(2)$

$\displaystyle H'(2) = \frac{1}{2\sqrt{4}}(-1)$

$\displaystyle H'(2) = \frac{-1}{4}$

3).

H(x) = r(s(x))

differentiate, using chain rule,

H'(x) = r'(s(x)).s'(x)

H'(2) = r'(s(2)).s'(2)

H'(2) = r'(1).(3)

H'(2) = 3 . r'(1)

we need the value of r'(1) to find H'(2).

4) You try this part. Did you get it ???