Please can some one help me with these 3 Problems I am lost...
I Greatly Appreciated!
Find f’(x) and simplify
f(x) = (x^2-1/ √x)^4
f(x) = e^-x-1/ e^-x+1
Find an equation of the line tangent to the graph of
f(x) = x ln x at x = 1
Please can some one help me with these 3 Problems I am lost...
I Greatly Appreciated!
Find f’(x) and simplify
f(x) = (x^2-1/ √x)^4
f(x) = e^-x-1/ e^-x+1
Find an equation of the line tangent to the graph of
f(x) = x ln x at x = 1
1) $\displaystyle f(x) = \left(\frac{(x^2 -1)}{\sqrt{x}}\right)^4$
1: Distribute the power of 4.
$\displaystyle f(x) = \left(\frac{(x^2 - 1)^4}{\sqrt{x}^4}\right)$
2: Simplify the denominator:
$\displaystyle f(x) = \left(\frac{(x^2 - 1)^4}{x^2}\right)$
3: Use the following rule:
$\displaystyle \frac{d}{dx}\left[\frac{u}{v}\right] = \frac{u'v - vu'}{v^2}$
4: Solve:
$\displaystyle f'(x) = \frac{8x(x^2 - 1)^3*x^2 - (x^2 - 1)^4*2x}{x^4}$
5. Simplify:
$\displaystyle f'(x) = 2x(x^2 - 1)^3\frac{4x^2 - (x^2 - 1)}{x^4}$
$\displaystyle f'(x) = 2x(x^2 - 1)^3\frac{3x^2 + 1}{x^4}$