Differentiate: f(x) = (x)(√(x^2+5))

[Nawz]

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)

=x³/(x²+5)^1/2+(x²+5)^1/2

I'm having problems simplifying. The answer in the back of the book is 2x^2 + 5 / Square root of x^2+5..

 

[Mark44]

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)

The above is correct, but you made a mistake in the next line.

=x³/(x²+5)^1/2+(x²+5)^1/2

This should be $$\frac{x^2}{(x^2 + 5)^{1/2}} + (x^2 + 5)^{1/2}$$

You can take a factor of 1/(x² + 5)^1/2 from both terms above.

I'm having problems simplifying. The answer in the back of the book is 2x^2 + 5 / Square root of x^2+5..

 

[Nawz]

Thank You! Thank You!