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

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

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

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

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

\frac{d x}{d x} = 1

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

Simplify

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

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

\int (2 x - 1)^{\frac{1}{2}} d x

d er i v a t i v e (7 x + 3)^{2}

y^{^{''}} - 4 y^{^{'}} + 3 y = 2 cos (3 t)

\frac{d}{d x} ((6 x)^{6 x})

\int \frac{4 ln ( x )}{x ^{3}} d x

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