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Popular >

derivative of x/(x-9)

Solution

\frac{d}{d x} (\frac{x}{x - 9})

Solution

- \frac{9}{( x - 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x - 9})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x - 9 ) - \frac{d}{d x} ( x - 9 ) x}{( x - 9 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x - 9) = 1

= \frac{1 \cdot ( x - 9 ) - 1 \cdot x}{( x - 9 ) ^{2}}

Simplify

\frac{1 \cdot ( x - 9 ) - 1 \cdot x}{( x - 9 ) ^{2}} : - \frac{9}{( x - 9 ) ^{2}}

= - \frac{9}{( x - 9 ) ^{2}}

Popular Examples

integral of (3x-5)^{1/2}

\int (3 x - 5)^{\frac{1}{2}} d x

y^{^{''}} = 6 x - 12

area y=6x^4-6x^2,y=3x^2 area

y = 6 x^{4} - 6 x^{2}, y = 3 x^{2}

(d^2x)/(dt^2)+2(dx)/(dt)+2x=sin(2t)

\frac{d ^{2} x}{d t ^{2}} + 2 \frac{d x}{d t} + 2 x = sin (2 t)

(dy)/(dx)= 1/(2cos^2(x))

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

Frequently Asked Questions (FAQ)

What is the derivative of x/(x-9) ?
The derivative of x/(x-9) is -9/((x-9)^2)
What is the first derivative of x/(x-9) ?
The first derivative of x/(x-9) is -9/((x-9)^2)