# The relationship between f and g is given. Explain the

The relationship between f and g is given. Explain the relationship between f′ and g′
$$\displaystyle{g{{\left({x}\right)}}}={2}{f{{\left({x}\right)}}}$$

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Sculd1987
Step 1
Given g(x)=2f(x).........(1)
we have to find the relation between their respective derivatives g'(x) and f'(x)
Step 2
Differentiating (1) with respect to x,
$$\displaystyle{\frac{{{d}{\left\lbrace{g{{\left({x}\right)}}}\right\rbrace}}}{{{\left.{d}{x}\right.}}}}={\frac{{{d}{\left\lbrace{2}{f{{\left({x}\right)}}}\right\rbrace}}}{{{\left.{d}{x}\right.}}}}$$
$$\displaystyle\Rightarrow{g}'{\left({x}\right)}={2}{\frac{{{d}{\left\lbrace{2}{f{{\left({x}\right)}}}\right\rbrace}}}{{{\left.{d}{x}\right.}}}}$$
=2f'(x)
Hence g' is 2 times f'.