Question

if y-sin^-1(5x), then dy/dx = ??

Answer 1

$$y = \sin^{-1}(5x)$$
What is the derivative of \(5x\), and what is the derivative of \(\sin x\)?

Answer 2

5 and cosx?

Answer 3

but it is the inverse of sin

Answer 4

\[\arcsin(x) \neq (\sin(x))^{-1}\]

Answer 5

\[\frac{ d }{ dx }\arcsin(x) = \frac{ 1 }{ \sqrt{1 - x^2} }\]

\[\frac{ d }{ dx }\arcsin(5x) = \frac{ 1 }{ \sqrt{1 - (5x)^2} }\left( \frac{ d }{ dx }(5x) \right) = \frac{ 5 }{ \sqrt{1 - 25x^2} }\]

Answer 6

ooh, thanks :)

Answer 7

remember that chain rule is ALWAYS used. except sometimes, you just end up multiplying by one.

Answer 8

okay

Answer 9

i'll remember