using the composite rule to differentiate function

[confusedbymath]

i need help in answering this question, preferably not just the answer but the working too. thankyou

Use the composite rule to differentiate the function:

f(x) = allsqrt 10 + x^2

 

[stapel]

Use the composite rule to differentiate the function:

f(x) = allsqrt 10 + x^2

What is your book's definition of its "composite rule"? How far have you gotten in applying this rule?

Please be complete. Thank you!

Eliz.

 

[skeeter]

\(\displaystyle f(x) = \sqrt{10 + x^2}\)

rewrite f(x) using an exponent ...

\(\displaystyle f(x) = (10 + x^2)^{\frac{1}{2}}\)

take the derivative using the power rule and the chain rule ...

\(\displaystyle f'(x) = \frac{1}{2}(10 + x^2)^{-\frac{1}{2}} \cdot 2x\)

simplify and change back to radical form ...

\(\displaystyle f'(x) = \frac{x}{\sqrt{10 + x^2}}\)