Match the following 1/f(x), [f(x)]^n, e^f(x), f(g(x))

Question

(i) Match the following

A - y =	B - \(\frac{dy}{dx}\)
\(\frac{1}{f(x)}\)	f'(x). e\(f(x)\)
[f(x)]n	f'(g(x)). g'(x)
e\(f(x)\)	\(-\frac{f'(x)}{[f(x)]^2}\)
f(g(x))	n(f(x))n-1f(x)
	n(f(x))n-1 f'(x)

Differentiate the following
(ii) y =\(\frac{1}{5x^2+3x+7}\) 
(iii) y = 3cosec⁴(7x) 
(iv) y = e^{2log tan 5x} 

Answer 1

(i)

A - y =	B - \(\frac{dy}{dx}\)
\(\frac{1}{f(x)}\)	\(-\frac{f'(x)}{[f(x)]^2}\)
[f(x)]n	n(f(x))n-1 f'(x)
e\(f(x)\)	f'(x).ef(x)
f(g(x))	f'(g(x)).g'(x)

  (ii) Given,  

(iii) Given, 

(iv) Given,