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Popular >

derivative of (x^2+9)/(x+3)

Solution

derivative of

\frac{x ^{2} + 9}{x + 3}

Solution

\frac{x ^{2} + 6 x - 9}{( x + 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 9}{x + 3})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} + 9 ) ( x + 3 ) - \frac{d}{d x} ( x + 3 ) ( x ^{2} + 9 )}{( x + 3 ) ^{2}}

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

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

= \frac{2 x ( x + 3 ) - 1 \cdot ( x ^{2} + 9 )}{( x + 3 ) ^{2}}

Simplify

\frac{2 x ( x + 3 ) - 1 \cdot ( x ^{2} + 9 )}{( x + 3 ) ^{2}} : \frac{x ^{2} + 6 x - 9}{( x + 3 ) ^{2}}

= \frac{x ^{2} + 6 x - 9}{( x + 3 ) ^{2}}

Popular Examples

integral from 0 to 2 of 1/(sqrt(4+x^2))

\int_{0}^{2} \frac{1}{4 + x ^{2}} d x

tangent of f(x)= 2/(x+1),\at x=1 tangent of

f (x) = \frac{2}{x + 1}, at x = 1

limit as x approaches 1 of sqrt(x^2-x)

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

derivative of (s^2-8s+15)/(s^2+3s+2)derivative of

\frac{s ^{2} - 8 s + 15}{s ^{2} + 3 s + 2}

derivative of sqrt((x^2/4+y^2-1))

\frac{d}{d x} (\frac{x ^{2}}{4} + y^{2} - 1)

Frequently Asked Questions (FAQ)

What is the derivative of (x^2+9)/(x+3) ?
The derivative of (x^2+9)/(x+3) is (x^2+6x-9)/((x+3)^2)
What is the first derivative of (x^2+9)/(x+3) ?
The first derivative of (x^2+9)/(x+3) is (x^2+6x-9)/((x+3)^2)