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Popular >

derivative of y=(f(x))/(x^2+2)

Solution

derivative of

y = \frac{f ( x )}{x ^{2} + 2}

Solution

\frac{\frac{df}{d x} ( x ^{2} + 2 ) - 2 x f ( x )}{( x ^{2} + 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

Popular Examples

(\partial)/(\partial L)(L^{1/4})

\frac{\partial}{\partial L} (L^{\frac{1}{4}})

integral of (2-8x)/(sqrt(81-4x^2))

\int \frac{2 - 8 x}{81 - 4 x ^{2}} d x

(dx)/(dt)=c_{1}x-c_{2}x^2

\frac{d x}{d t} = c_{1} x - c_{2} x^{2}

integral from-1 to 2 of 3/(x^2)

\int_{- 1}^{2} \frac{3}{x ^{2}} d x

sum from n=0 to infinity of 5^n

n = 0 \sum \infty 5^{n}

Frequently Asked Questions (FAQ)

What is the derivative of y=(f(x))/(x^2+2) ?
The derivative of y=(f(x))/(x^2+2) is (\frac{df)/(dx)(x^2+2)-2xf(x)}{(x^2+2)^2}
What is the first derivative of y=(f(x))/(x^2+2) ?
The first derivative of y=(f(x))/(x^2+2) is (\frac{df)/(dx)(x^2+2)-2xf(x)}{(x^2+2)^2}