What are the critical points of $f (x) = e^{x^{\frac{1}{3}}} \cdot \sqrt{x + 8}$ $f(x) = e^(x^(1/3))*sqrt(x+8)$ ?

Question

What are the critical points of $f (x) = e^{x^{\frac{1}{3}}} \cdot \sqrt{x + 8}$ $f(x) = e^(x^(1/3))*sqrt(x+8)$ ?

1 Answer

Impact of this question

1793 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-08T09:02:37

${f (x)}^{/} =$ $f(x)^/=$ $(3)$ $(3)$ $(1)$ $(1)$ $+$ $+$ $(2)$ $(2)$ $(4)$ $(4)$

please see below !

Explanation:

$f (x) = e^{x^{\frac{1}{3}}} \cdot \sqrt{x + 8}$ $f(x)=e^(x^(1/3))*sqrt(x+8)$

$y = \sqrt{x + 8}$ $y=sqrt(x+8)$ $(1)$ $(1)$

$z = e^{x^{\frac{1}{3}}}$ $z=e^(x^(1/3))$ $(2)$ $(2)$

$f (x) = z \cdot y$ $f(x)=z*y$

${f (x)}^{/} = z^{/} \cdot y + z \cdot y^{/}$ $f(x)^/=z^/*y+z*y^/$

$z = e^{x^{\frac{1}{3}}}$ $z=e^(x^(1/3))$

$x^{\frac{1}{3}} = n$ $x^(1/3)=n$

$z = e^{n}$ $z=e^n$

$x^{\frac{1}{3}} = n$ $x^(1/3)=n$

$\frac{d n}{d x} = \frac{1}{3} x^{- \frac{2}{3}}$ $(dn)/dx=1/3x^(-2/3)$

$z = e^{n}$ $z=e^n$

$\frac{d z}{d n} = e^{n}$ $dz/(dn)=e^n$

$\frac{d z}{d n} \cdot \frac{d n}{d x}$ $(dz)/(dn) * (dn)/dx$ = $\frac{d z}{d x}$ $(dz)/dx$

$\frac{d z}{d x} =$ $(dz)/dx=$ $\frac{1}{3} x^{- \frac{2}{3}} \cdot e^{x^{\frac{1}{3}}}$ $1/3x^(-2/3)*e^(x^(1/3))$ $(3)$ $(3)$

$y = \sqrt{x + 8}$ $y=sqrt(x+8)$

$u = x + 8$ $u=x+8$

$\frac{d u}{d x} = 1$ $(du)/(dx)=1$

$y = \sqrt{u}$ $y=sqrt(u)$

$\frac{d y}{d u} = \frac{1}{2} u^{- \frac{1}{2}}$ $dy/(du)=1/2u^(-1/2)$

$\frac{d y}{d u} \cdot$ $dy/(du)*$ $\frac{d u}{d x}$ $(du)/(dx)$ $= \frac{d y}{d x}$ $=dy/dx$

$\frac{d y}{d x} = \frac{1}{2} {(x + 8)}^{- \frac{1}{2}}$ $dy/dx=1/2(x+8)^(-1/2)$ $(4)$ $(4)$

${f (x)}^{/} = z^{/} \cdot y + z \cdot y^{/}$ $f(x)^/=z^/*y+z*y^/$

${f (x)}^{/} =$ $f(x)^/=$ $(3)$ $(3)$ $(1)$ $(1)$ $+$ $+$ $(2)$ $(2)$ $(4)$ $(4)$

Science

Math

Humanities

... and beyond

What are the critical points of $f (x) = e^{x^{\frac{1}{3}}} \cdot \sqrt{x + 8}$ $f(x) = e^(x^(1/3))*sqrt(x+8)$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What are the critical points of f(x)=ex13⋅√x+8 f(x) = e^(x^(1/3))*sqrt(x+8)?

1 Answer

Explanation:

Related questions

Impact of this question

What are the critical points of $f (x) = e^{x^{\frac{1}{3}}} \cdot \sqrt{x + 8}$ $f(x) = e^(x^(1/3))*sqrt(x+8)$ ?