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

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

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

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

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

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

Solution steps

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

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

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

\frac{\partial}{\partial x} ((x + 2 y)^{2})

f (x) = ln (x^{3})

\int ∣ 2 x - 1 ∣ d x

\int \frac{1}{5 x ^{2} - 20 x + 100} d x

\frac{\partial}{\partial y} (e^{x - 2} - y)

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