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

The derivative of (sin(x)/(tan(x)+x)) is (cos(x)(tan(x)+x)-(sec^2(x)+1)sin(x))/((tan(x)+x)^2)

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

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

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\frac{d}{d x} (\frac{sin ( x )}{tan ( x ) + x})

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

Solution steps

\frac{d}{d x} (\frac{sin ( x )}{tan ( x ) + x})

Apply the Quotient Rule:

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

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

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

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

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

\frac{1}{( 3 x + 7 )}

\frac{1}{4 + 3 x}

\frac{d}{d x} (ln (x + a))

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

\frac{d}{d x} (e^{x^{3}})

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