What is the derivative of (cos(3x^6)/(2x)) ?

The derivative of (cos(3x^6)/(2x)) is (5cos(3)x^4)/2

What is the first derivative of (cos(3x^6)/(2x)) ?

The first derivative of (cos(3x^6)/(2x)) is (5cos(3)x^4)/2

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\frac{d}{d x} (\frac{cos ( 3 ) x ^{6}}{2 x})

\frac{5 cos ( 3 ) x ^{4}}{2}

Solution steps

\frac{d}{d x} (\frac{cos ( 3 ) x ^{6}}{2 x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{cos ( 3 )}{2} \frac{d}{d x} (\frac{x ^{6}}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{cos ( 3 )}{2} \cdot \frac{\frac{d}{d x} ( x ^{6} ) x - \frac{d x}{d x} x ^{6}}{x ^{2}}

\frac{d}{d x} (x^{6}) = 6 x^{5}

\frac{d x}{d x} = 1

= \frac{cos ( 3 )}{2} \cdot \frac{6 x ^{5} x - 1 \cdot x ^{6}}{x ^{2}}

Simplify

\frac{cos ( 3 )}{2} \cdot \frac{6 x ^{5} x - 1 \cdot x ^{6}}{x ^{2}} : \frac{5 cos ( 3 ) x ^{4}}{2}

= \frac{5 cos ( 3 ) x ^{4}}{2}

What is the derivative of (cos(3x^6)/(2x)) ?
The derivative of (cos(3x^6)/(2x)) is (5cos(3)x^4)/2
What is the first derivative of (cos(3x^6)/(2x)) ?
The first derivative of (cos(3x^6)/(2x)) is (5cos(3)x^4)/2