Question

find dy/dx of y=sqrt(lnx) and of y=cos(ln2x^2)

Answer 1

hI!!

Answer 2

chain rule for both

Answer 3

i ended up with (1)/(x^1/2) but i don't think it's right

Answer 4

\[(f\circ g)'=f(g)\times g'\] with \[f(x)=\sqrt{x}, f'(x)=\frac{1}{2\sqrt{x}}, g(x)=\ln(x), g'(x)=\frac{1}{x}\]

Answer 5

no that is not right

Answer 6

lets cut to the chase \[\frac{d}{dx}\sqrt{f(x)} =\frac{f'(x)}{2\sqrt{f(x)}}\]

Answer 7

why is it 2\[\sqrt{f(x)}\]

Answer 8

the derivative of the square root of x is one over two square root of x

Answer 9

therefore, by the chain rule, the derivative of the square root of something, is one over two square root of something, times the derivative of something

Answer 10

so what if f prime of x? x^.5?

Answer 11

for example, the derivative of \[f(x)=\sqrt{\sin(x)}\] is \[\frac{\cos(x)}{2\sqrt{\sin(x)}}\]

Answer 12

same thing .5=1/2

Answer 13

x^(1/2) = sqrt(x)

Answer 14

forget exponential notation, just memorize it

Answer 15

here let me show you why.

Answer 16

\[f(x)=\sqrt{x}\\
f'(x)=\frac{1}{2\sqrt{x}}\] it is always the same, like \(7\times 8=56\) alway s

Answer 17

the square root is a very very (very) common function, just know it so you can access it any time
forget the power rule, that is just a gimmick

Answer 18

so the derivative of y = sqrt(lnx) is: 1/2sqrt(x) ?

Answer 19

hmm no

Answer 20

(1/\[\sqrt{x}\])