What is the derivative of (1+sin(x)/(xcos(x))) ?

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

What is the first derivative of (1+sin(x)/(xcos(x))) ?

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

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\frac{d}{d x} (\frac{1 + sin ( x )}{x cos ( x )})

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

Solution steps

\frac{d}{d x} (\frac{1 + sin ( x )}{x cos ( x )})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (1 + sin (x)) = cos (x)

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

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

Simplify

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

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

x \to 1 lim (3^{(\frac{1}{x})})

3 sin (3 t + 2)

\int 4 x^{3} e^{2 x^{4}} d x

\frac{d}{d x} ((\frac{x ^{2}}{6 - x})^{5})

\int_{0}^{1} x^{4} - 2 x^{3} + x^{2} d x

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