What is expand ((4t+1)y'(t))/t ?

The solution to expand ((4t+1)y'(t))/t is 4y'(t)+(y'(t))/t

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expand ((4t+1)y'(t))/t

expand

\frac{( 4 t + 1 ) y ^{'} ( t )}{t}

4 y' (t) + \frac{y ' ( t )}{t}

Solution steps

\frac{( 4 t + 1 ) y ^{'} ( t )}{t}

Expand

(4 t + 1) y^{'} (t) : 4 t y^{'} (t) + y^{'} (t)

= \frac{4 t y ^{'} ( t ) + y ^{'} ( t )}{t}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{4 t y ^{'} ( t ) + y ^{'} ( t )}{t} = \frac{4 t y ^{'} ( t )}{t} + \frac{y ^{'} ( t )}{t}

= \frac{4 t y ^{^{'}} ( t )}{t} + \frac{y ^{^{'}} ( t )}{t}

Cancel

\frac{4 t y ^{'} ( t )}{t} : 4 y^{'} (t)

= 4 y^{^{'}} (t) + \frac{y ^{^{'}} ( t )}{t}

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What is expand ((4t+1)y'(t))/t ?
The solution to expand ((4t+1)y'(t))/t is 4y'(t)+(y'(t))/t