What is the ((g(t))/(f(t)))' ?

The ((g(t))/(f(t)))' is (g'(t)f(t)-f'(t)g(t))/(f(t)^2)

What is the first ((g(t))/(f(t)))' ?

The first ((g(t))/(f(t)))' is (g'(t)f(t)-f'(t)g(t))/(f(t)^2)

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(\frac{g ( t )}{f ( t )})^{'}

\frac{g ' ( t ) f ( t ) - f ' ( t ) g ( t )}{f ( t ) ^{2}}

Solution steps

(\frac{g ( t )}{f ( t )})^{'}

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{g ^{^{'}} ( t ) f ( t ) - f ^{^{'}} ( t ) g ( t )}{f ( t ) ^{2}}

= \frac{g ^{^{'}} ( t ) f ( t ) - f ^{^{'}} ( t ) g ( t )}{f ( t ) ^{2}}

ln (1 - x^{2})

\frac{d}{d x} (a e^{- a x})

\frac{d}{d x} (sin (- 6 x))

\int (2 x - 5) e^{x} d x

x \to 0 + lim (2 x^{x})

What is the ((g(t))/(f(t)))' ?
The ((g(t))/(f(t)))' is (g'(t)f(t)-f'(t)g(t))/(f(t)^2)
What is the first ((g(t))/(f(t)))' ?
The first ((g(t))/(f(t)))' is (g'(t)f(t)-f'(t)g(t))/(f(t)^2)