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Popular >

derivative of y=(f(x))/(g(x))

Solution

derivative of

y = \frac{f ( x )}{g ( x )}

Solution

\frac{\frac{df}{d x} g ( x ) - \frac{d g}{d x} f ( x )}{g ( x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{f ( x )}{g ( x )})

Apply the Quotient Rule:

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

= \frac{\frac{df}{d x} g ( x ) - \frac{d g}{d x} f ( x )}{g ( x ) ^{2}}

= \frac{\frac{df}{d x} g ( x ) - \frac{d g}{d x} f ( x )}{g ( x ) ^{2}}

Popular Examples

(\partial)/(\partial y)(x^2y+4y-7)

\frac{\partial}{\partial y} (x^{2} y + 4 y - 7)

f(x)=(2x-3)^{ln(x)}

f (x) = (2 x - 3)^{l n (x)}

integral of (x^{1.1}+7x^{2.5})

\int (x^{1.1} + 7 x^{2.5}) d x

limit as x approaches 2 of 3x^3-1

x \to 2 lim (3 x^{3} - 1)

(\partial)/(\partial t)(tan(t))

\frac{\partial}{\partial t} (tan (t))

Frequently Asked Questions (FAQ)

What is the derivative of y=(f(x))/(g(x)) ?
The derivative of y=(f(x))/(g(x)) is (\frac{df)/(dx)g(x)-(dg)/(dx)f(x)}{g(x)^2}
What is the first derivative of y=(f(x))/(g(x)) ?
The first derivative of y=(f(x))/(g(x)) is (\frac{df)/(dx)g(x)-(dg)/(dx)f(x)}{g(x)^2}