The discussion focuses on differentiating the function f(x) = x√(x² + 5). The correct derivative is f'(x) = (x²/(x² + 5)^(1/2)) + (x² + 5)^(1/2). Participants clarify that a common factor of 1/(x² + 5)^(1/2) can be factored out from both terms to simplify the expression. The final answer, as provided in the textbook, is (2x² + 5)/(√(x² + 5)).
PREREQUISITESStudents studying calculus, particularly those focusing on differentiation techniques, as well as educators seeking to clarify concepts related to product and chain rules.
The above is correct, but you made a mistake in the next line.Nawz said:Homework Statement
Differentiate.
f(x) = (x) (square root of (x2+5))
Homework Equations
The Attempt at a Solution
f(x) = (x) (square root of (x2+5))
=(x)(x2+5)1/2
f'(x)=(x)1/2(x2+5)-1/2(2x)+(1)(x2+5)
This should be [tex]\frac{x^2}{(x^2 + 5)^{1/2}} + (x^2 + 5)^{1/2}[/tex]Nawz said:=x3/(x2+5)1/2+(x2+5)1/2
Nawz said:I'm having problems simplifying. The answer in the back of the book is 2x^2 + 5 / Square root of x^2+5..