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

The derivative of ((tan(x)/x)^2) is (2tan(x)(xsec^2(x)-tan(x)))/(x^3)

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

The first derivative of ((tan(x)/x)^2) is (2tan(x)(xsec^2(x)-tan(x)))/(x^3)

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

\frac{2 tan ( x ) ( x sec ^{2} ( x ) - tan ( x ) )}{x ^{3}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{tan ( x )}{x}) = \frac{x sec ^{2} ( x ) - tan ( x )}{x ^{2}}

= 2 \cdot \frac{tan ( x )}{x} \cdot \frac{x sec ^{2} ( x ) - tan ( x )}{x ^{2}}

Simplify

2 \cdot \frac{tan ( x )}{x} \cdot \frac{x sec ^{2} ( x ) - tan ( x )}{x ^{2}} : \frac{2 tan ( x ) ( x sec ^{2} ( x ) - tan ( x ) )}{x ^{3}}

= \frac{2 tan ( x ) ( x sec ^{2} ( x ) - tan ( x ) )}{x ^{3}}

\int \frac{x - 6}{( x + 3 ) ^{2} + 36} d x

n = 1 \sum \infty n ln (2)

\int sin^{2} (v) cos^{3} (v) d v

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

\frac{d y}{d x}, x y = 15

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