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Popular >

(x/(x^2+9))^'

Solution

(\frac{x}{x ^{2} + 9})^{^{'}}

Solution

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

Solution steps

(\frac{x}{x ^{2} + 9})^{'}

Apply the Quotient Rule:

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

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

x^{'} = 1

(x^{2} + 9)^{'} = 2 x

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

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

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

Popular Examples

(\partial)/(\partial x)(x^2+xy+y^2-2x-5y)

\frac{\partial}{\partial x} (x^{2} + x y + y^{2} - 2 x - 5 y)

derivative of f(x)=e^{5x^2-x}derivative of

f (x) = e^{5 x^{2} - x}

derivative of (3x^5-7x^2-4/(x^2))

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\frac{d}{d x} (\frac{2 x ^{3} - 4 x ^{2} + 3}{x ^{2}})

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

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

Frequently Asked Questions (FAQ)

What is the (x/(x^2+9))^' ?
The (x/(x^2+9))^' is (-x^2+9)/((x^2+9)^2)
What is the first (x/(x^2+9))^' ?
The first (x/(x^2+9))^' is (-x^2+9)/((x^2+9)^2)