What is the derivative of (sin(x)/(x^2-1)) ?

The derivative of (sin(x)/(x^2-1)) is (cos(x)(x^2-1)-2xsin(x))/((x^2-1)^2)

What is the first derivative of (sin(x)/(x^2-1)) ?

The first derivative of (sin(x)/(x^2-1)) is (cos(x)(x^2-1)-2xsin(x))/((x^2-1)^2)

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

\frac{cos ( x ) ( x ^{2} - 1 ) - 2 x sin ( x )}{( x ^{2} - 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (sin (x)) = cos (x)

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

= \frac{cos ( x ) ( x ^{2} - 1 ) - 2 x sin ( x )}{( x ^{2} - 1 ) ^{2}}

y = 14 x sin (x), (\frac{π}{2}, 7 π)

x \to \infty lim (xx)

\int 3 cos^{3} (6 x) d x

\int cos^{10} (2 y) sin^{3} (2 y) d y

\frac{d}{d x} (\frac{1}{9} x - ln (3 x))

What is the derivative of (sin(x)/(x^2-1)) ?
The derivative of (sin(x)/(x^2-1)) is (cos(x)(x^2-1)-2xsin(x))/((x^2-1)^2)
What is the first derivative of (sin(x)/(x^2-1)) ?
The first derivative of (sin(x)/(x^2-1)) is (cos(x)(x^2-1)-2xsin(x))/((x^2-1)^2)