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

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

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

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

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derivative of

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

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

Solution steps

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

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

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

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

Simplify

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

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

\int \frac{1 + x + x}{x} d x

\frac{d y}{d x} = \frac{13 x}{y}

x ∣ x ∣

\int \frac{3 x}{1} d x

n = 1 \sum \infty 2 n + 1

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