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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( y - 1 ) - \frac{d}{d x} ( y - 1 ) x ^{2}}{( y - 1 ) ^{2}}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (y - 1) = \frac{d y}{d x}

= \frac{2 x ( y - 1 ) - \frac{d y}{d x} x ^{2}}{( y - 1 ) ^{2}}

Popular Examples

derivative of (sinh(x^2)^{1/x})

\frac{d}{d x} ((sinh (x^{2}))^{\frac{1}{x}})

(\partial)/(\partial y)(5x^4y)

\frac{\partial}{\partial y} (5 x^{4} y)

derivative of 5^x-1

\frac{d}{d x} (5^{x} - 1)

derivative of (sin(x)+cos(x))/(e^x)derivative of

\frac{sin ( x ) + cos ( x )}{e ^{x}}

integral of (3x+1)(3x^2+2x)^{1/3}

\int (3 x + 1) (3 x^{2} + 2 x)^{\frac{1}{3}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^2/(y-1)) ?
The derivative of (x^2/(y-1)) is (2x(y-1)-\frac{dy)/(dx)x^2}{(y-1)^2}
What is the first derivative of (x^2/(y-1)) ?
The first derivative of (x^2/(y-1)) is (2x(y-1)-\frac{dy)/(dx)x^2}{(y-1)^2}