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

The derivative of sin((x-3)/(2x)) is (3cos(\frac{x-3)/(2x))}{2x^2}

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

The first derivative of sin((x-3)/(2x)) is (3cos(\frac{x-3)/(2x))}{2x^2}

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derivative of

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

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

Solution steps

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

Apply the chain rule:

cos (\frac{x - 3}{2 x}) \frac{d}{d x} (\frac{x - 3}{2 x})

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\int_{- \infty}^{0} \frac{1}{6 - 3 x} d x

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

\frac{d}{d x} (ln (x^{6} - 1))

\frac{d}{d x} (e^{s i n (x)} cos (x))

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