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Popular >

derivative of x/(x^2+5)

Solution

derivative of

\frac{x}{x ^{2} + 5}

Solution

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

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x ^{2} + 5 ) - \frac{d}{d x} ( x ^{2} + 5 ) x}{( x ^{2} + 5 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 5) = 2 x

= \frac{1 \cdot ( x ^{2} + 5 ) - 2 xx}{( x ^{2} + 5 ) ^{2}}

1 \cdot (x^{2} + 5) - 2 xx = - x^{2} + 5

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

Popular Examples

integral of cos^{12}(x)sin^{15}(x)

\int cos^{12} (x) sin^{15} (x) d x

laplacetransform cos(15t)laplace transform

cos (15 t)

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

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

y^{''}+5y^'+6y=0,y(0)=2,y^'(0)=0

y^{^{''}} + 5 y^{^{'}} + 6 y = 0, y (0) = 2, y^{^{'}} (0) = 0

inverse oflaplace (1/(s+1)-1)/(s^2-1)inverse laplace

\frac{\frac{1}{s + 1} - 1}{s ^{2} - 1}

Frequently Asked Questions (FAQ)

What is the derivative of x/(x^2+5) ?
The derivative of x/(x^2+5) is (-x^2+5)/((x^2+5)^2)
What is the first derivative of x/(x^2+5) ?
The first derivative of x/(x^2+5) is (-x^2+5)/((x^2+5)^2)