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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 4 x^{\frac{2}{3}} d x

\frac{\partial}{\partial y} (3 x + 2 x y^{2})

\int \frac{4}{( x ^{2} + 5 x - 14 )} d x

x \to 2 lim (2 x^{2} - 3)

x \to - 1 + lim (\frac{1}{x ^{2} - 1})

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