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Popular >

((f(t))/(g(t)))'

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

Popular Examples

derivative of sqrt(x)e^{x^2}(x^2+1^{10})

\frac{d}{d x} (x e^{x^{2}} (x^{2} + 1)^{10})

x(dy)/(dx)=2x^2+y,y(1)=3

x \frac{d y}{d x} = 2 x^{2} + y, y (1) = 3

sum from n=2 to infinity of 1/(n^2+5n+6)

n = 2 \sum \infty \frac{1}{n ^{2} + 5 n + 6}

sum from n=1 to infinity of (5n)/(3n-1)

n = 1 \sum \infty \frac{5 n}{3 n - 1}

derivative of-(2x/(x-1))

\frac{d}{d x} (- \frac{2 x}{x - 1})

Frequently Asked Questions (FAQ)

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