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

The derivative of cos((3x^2/(x+2))) is -(3sin(\frac{3x^2)/(x+2))(x^2+4x)}{(x+2)^2}

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

The first derivative of cos((3x^2/(x+2))) is -(3sin(\frac{3x^2)/(x+2))(x^2+4x)}{(x+2)^2}

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

- \frac{3 sin ( \frac{3 x ^{2}}{x + 2} ) ( x ^{2} + 4 x )}{( x + 2 ) ^{2}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{3 x ^{2}}{x + 2}) = \frac{3 ( x ^{2} + 4 x )}{( x + 2 ) ^{2}}

= - sin (\frac{3 x ^{2}}{x + 2}) \frac{3 ( x ^{2} + 4 x )}{( x + 2 ) ^{2}}

Multiply fractions:

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

= - \frac{3 sin ( \frac{3 x ^{2}}{x + 2} ) ( x ^{2} + 4 x )}{( x + 2 ) ^{2}}

What is the derivative of cos((3x^2/(x+2))) ?
The derivative of cos((3x^2/(x+2))) is -(3sin(\frac{3x^2)/(x+2))(x^2+4x)}{(x+2)^2}
What is the first derivative of cos((3x^2/(x+2))) ?
The first derivative of cos((3x^2/(x+2))) is -(3sin(\frac{3x^2)/(x+2))(x^2+4x)}{(x+2)^2}