Question

If f and g are differentiable functions for all real values of x such that f(2) = 5, g(2) = 3, f '(2) = 1, g '(2) = -2, then find h '(2) if h(x) = f(x) g(x)

Answer 1

Hi !!!

h'(x) = f'(x) g(x) + f(x) g'(x) by product rule differentiation

put x =2

h'(2) = f'(2) g(2) + f(2) g'(2)

h'(2)= 1 × 3 + 5 × (-2)

h'(2) = 3-10

h'(2) = -7

Have a great future ahead...

Answer 2

$hlo \: here \: is \: your \: \: ans$
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⇩ ⇩ ⇩ ⇩


USING QUOTIENT FORMULA⇨

h'(x)=[g(x)f'(x)-f(x)g'(x)] / [g(x)^2

Given.

1.f(2)=5

2.g(2)=3

3.f'(2)=1

4.g'(2)=-2.

so. put value in the above formula b



we get


h'(2)=[g(2)f'(2)-f(2)g'(2)]/g(2)^2

=>[3×1. - 5× (-2)]/3^2


=>13/9