Question

differentiation of f(x)=1/√(18-x^2)​

Answer 1

Question:-To diffrentiate

$\frac{1}{ \sqrt{18 - {x}^{2} } }$

with respect to x

Solution:-

$\frac{1}{ \sqrt{18 - {x }^{2} } } = \frac{1}{ ({18 - {x}^{2} )}^{ \frac{1}{2} } } \\ = {(18 - x)}^{ \frac{ - 1}{2} }$

now, diffrentiate it using the chain rule

$\frac{df(x)}{dx} = \frac{ - 1}{2} {(18 - x)}^{ \frac{ - 3}{2} } \times (0 - 1) \\ \frac{df(x)}{dx} = \frac{1}{2} {(18 - x)}^{ \frac{ - 3}{2} } \\ this \: will \: be \: the \: required \: diffrentation$

$hope \: it \: helps \: u$