What is the derivative of (x^2+1/(xsin(x))) ?

The derivative of (x^2+1/(xsin(x))) is (x^2sin(x)-sin(x)-x^3cos(x)-xcos(x))/(x^2sin^2(x))

What is the first derivative of (x^2+1/(xsin(x))) ?

The first derivative of (x^2+1/(xsin(x))) is (x^2sin(x)-sin(x)-x^3cos(x)-xcos(x))/(x^2sin^2(x))

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

\frac{x ^{2} sin ( x ) - sin ( x ) - x ^{3} cos ( x ) - x cos ( x )}{x ^{2} sin ^{2} ( x )}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 xx sin ( x ) - ( sin ( x ) + x cos ( x ) ) ( x ^{2} + 1 )}{( x sin ( x ) ) ^{2}} : \frac{x ^{2} sin ( x ) - sin ( x ) - x ^{3} cos ( x ) - x cos ( x )}{x ^{2} sin ^{2} ( x )}

= \frac{x ^{2} sin ( x ) - sin ( x ) - x ^{3} cos ( x ) - x cos ( x )}{x ^{2} sin ^{2} ( x )}

\int (\frac{5}{x} + e^{x}) d x

x \to - 1.001 lim (x^{3} - 1)

\frac{d}{d x} (3 x^{3} - 6 x)

\frac{d}{d x} (cos (x - a))

\int_{0}^{\frac{1}{5}} x arcsin (5 x) d x

What is the derivative of (x^2+1/(xsin(x))) ?
The derivative of (x^2+1/(xsin(x))) is (x^2sin(x)-sin(x)-x^3cos(x)-xcos(x))/(x^2sin^2(x))
What is the first derivative of (x^2+1/(xsin(x))) ?
The first derivative of (x^2+1/(xsin(x))) is (x^2sin(x)-sin(x)-x^3cos(x)-xcos(x))/(x^2sin^2(x))