Question

Consider the following.
y=(sqrt8+3x)
(a) Write the composite function in the form f(g(x)) by identifying the inner function u = g(x) and the outer function y = f(u).
u = g(x) = ?
y = f(u) = ?

(b) Find the derivative dy/dx.
dy/dx = ?

Answer 1

can you show me step by step please

Answer 2

is this
\[y = \sqrt{8+3x}\]?

Answer 3

yes

Answer 4

ok then inner function
\[g(x)=8+3x\]

Answer 5

yes i got that

Answer 6

outer function
\[f(u)=\sqrt{u}\]

Answer 7

so what would that be

Answer 8

so if
\[u=8+3x\] you get
\[f(g(x))=f(u)=f(8+3x)=\sqrt{8+3x}\]

Answer 9

yes but whats u?

Answer 10

\[u=8+3x\]
\[\frac{du}{dx}=3\]

Answer 11

no its \[-22x(5-x^2)^10\]

Answer 12

\[\frac{dy}{du}=\frac{1}{2\sqrt{u}}\]

Answer 13

and therefore
\[\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}=\frac{1}{2\sqrt{u}}\times 3=\frac{3}{2\sqrt{8+3x}}\]

Answer 14

the original function was
\[f(x)=\sqrt{8+3x}\] and
\[f'(x)=\frac{3}{2\sqrt{8+3x}}\]

Answer 15

\[−22x(5−x^2)^{10}\] must be the answer to a different problem.

Answer 16

it is the answer to "what is the derivative of
\[f(x)=(5-x^2)^{11}\]

Answer 17

ok but ill get back to you when i see what i did