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

The derivative of (sin(x)/(3x^2)) is (xcos(x)-2sin(x))/(3x^3)

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

The first derivative of (sin(x)/(3x^2)) is (xcos(x)-2sin(x))/(3x^3)

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to 3 lim (g (x))

g (x) = (x - 4)^{3} + 3 x (x - 4)^{2}

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

\frac{a}{s}

x = y^{4}, y = - x^{5}

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