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Popular >

derivative of (x+3/(x-3))

Solution

\frac{d}{d x} (\frac{x + 3}{x - 3})

Solution

- \frac{6}{( x - 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x + 3}{x - 3})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 3 ) ( x - 3 ) - \frac{d}{d x} ( x - 3 ) ( x + 3 )}{( x - 3 ) ^{2}}

\frac{d}{d x} (x + 3) = 1

\frac{d}{d x} (x - 3) = 1

= \frac{1 \cdot ( x - 3 ) - 1 \cdot ( x + 3 )}{( x - 3 ) ^{2}}

Simplify

\frac{1 \cdot ( x - 3 ) - 1 \cdot ( x + 3 )}{( x - 3 ) ^{2}} : - \frac{6}{( x - 3 ) ^{2}}

= - \frac{6}{( x - 3 ) ^{2}}

Popular Examples

derivative of x^2*ln(x)derivative of

x^{2} \cdot ln (x)

integral of (3x^2)/(sqrt(x^2-4))

\int \frac{3 x ^{2}}{x ^{2} - 4} d x

integral of sin(2y)(3-cos(2y))^2

\int sin (2 y) (3 - cos (2 y))^{2} d y

tangent of (x-1)/(x+1)tangent of

\frac{x - 1}{x + 1}

integral from 0 to 1 of 6x(1-x)

\int_{0}^{1} 6 x (1 - x) d x

Frequently Asked Questions (FAQ)

What is the derivative of (x+3/(x-3)) ?
The derivative of (x+3/(x-3)) is -6/((x-3)^2)
What is the first derivative of (x+3/(x-3)) ?
The first derivative of (x+3/(x-3)) is -6/((x-3)^2)