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Popular >

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

Solution

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

Solution

\frac{10 x}{( x ^{2} + 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x^{2} + 1) = 2 x

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

Expand

2 x (x^{2} + 1) - 2 x (x^{2} - 4) : 10 x

= \frac{10 x}{( x ^{2} + 1 ) ^{2}}

Popular Examples

derivative of y=220+65x derivative of

y = 220 + 65 x

derivative of f(x)= x/(x+8)derivative of

f (x) = \frac{x}{x + 8}

(15xy^2-4y)+(15x^2y-4x)y^'=0

(15 x y^{2} - 4 y) + (15 x^{2} y - 4 x) y^{^{'}} = 0

sum from n=1 to infinity of 1/(2^n-1)

n = 1 \sum \infty \frac{1}{2 ^{n} - 1}

d/(dt)(-1/(2(t+1) 3/2))

\frac{d}{d t} (- \frac{1}{2 ( t + 1 ) \frac{3}{2}})

Frequently Asked Questions (FAQ)

What is the derivative of (x^2-4/(x^2+1)) ?
The derivative of (x^2-4/(x^2+1)) is (10x)/((x^2+1)^2)
What is the first derivative of (x^2-4/(x^2+1)) ?
The first derivative of (x^2-4/(x^2+1)) is (10x)/((x^2+1)^2)