What is the derivative of (sin(3x)/(1+x^2)) ?

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

What is the first derivative of (sin(3x)/(1+x^2)) ?

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

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\frac{d}{d x} (\frac{sin ( 3 x )}{1 + x ^{2}})

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

Solution steps

\frac{d}{d x} (\frac{sin ( 3 x )}{1 + x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( sin ( 3 x ) ) ( 1 + x ^{2} ) - \frac{d}{d x} ( 1 + x ^{2} ) sin ( 3 x )}{( 1 + x ^{2} ) ^{2}}

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

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

= \frac{cos ( 3 x ) \cdot 3 ( 1 + x ^{2} ) - 2 x sin ( 3 x )}{( 1 + x ^{2} ) ^{2}}

\frac{\partial}{\partial x} (10 cos (x) y^{2} z)

3 x^{2} e^{x} + e^{x} (x^{3} + 6)

\frac{\partial}{\partial y} (9 e^{x} ln (y))

\frac{d}{d x} (\frac{5 x ^{2} - x ^{4}}{9})

n = 1 \sum \infty 1 + \frac{1}{n}

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