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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

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

d er i v a t i v e y = \frac{x}{( x + 1 ) ^{\frac{1}{2}}}

\frac{d}{d t} (t^{2} + t^{3})

\frac{d}{d x} (2 cos (3 x) + 2 sin (10 y) + 3 x - 10 y)

d er i v a t i v e \frac{( x ^{2} + 3 )}{( x + 1 )}

d er i v a t i v e 2 tan (x) + sec (x) - 3 cot (x)

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