Match the following A- function log f(x), f(x)/g(x),y^2,x^2

Question

(i) Match the following :

A - Function	B - Derivative w.r.t to x
log f(x)	2x
\(\frac{f(x)}{g(x)}\)	\(\frac{f'(x)}{g'(x)}\)
y2	\(\frac{g(x).f'(x) - g'(x).f(x)}{[g(x)]^2}\)
x2	\(\frac{f'(x)}{f(x)}\)
	\(2y \frac{dy}{dx}\)

(ii) If log (x² + y²) = 2 tan^-1 \(\frac{y}{x}\), then show that \(\frac{dy}{dx}\) = \(\frac{x+y}{x-y}\)

Answer 1

(i)

A - Function	B - Derivative w.r.t to x
log f(x)	\(\frac{f'(x)}{f(x)}\)
\(\frac{f(x)}{g(x)}\)	\(\frac{g(x).f'(x) - g'(x).f(x)}{[g(x)]^2}\)
y2	\(2y \frac{dy}{dx}\)
x2	2x

 

(ii) Given, 

log (x² + y²) = 2 tan^-1(\(\frac{y}{x}\)).
Differentiate w.r.to x, we get;