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

The derivative of cos(x/(sqrt(x+2))) is -(sin(x/(sqrt(x+2)))(x+4))/(2(x+2)sqrt(x+2))

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

The first derivative of cos(x/(sqrt(x+2))) is -(sin(x/(sqrt(x+2)))(x+4))/(2(x+2)sqrt(x+2))

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derivative of

cos (\frac{x}{x + 2})

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

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

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

\int \frac{1}{x 1 + x ^{4}} d x

f (x) = \frac{1}{( 2 x + 1 ) ^{2}}

\frac{d y}{d x} = \frac{7 x + 2 y}{7 x + 2 y + 2}

f (x) = 2 - 7 x, (- 2, 4)

\frac{d}{d x} (∣ cos (x) ∣)

What is the derivative of cos(x/(sqrt(x+2))) ?
The derivative of cos(x/(sqrt(x+2))) is -(sin(x/(sqrt(x+2)))(x+4))/(2(x+2)sqrt(x+2))
What is the first derivative of cos(x/(sqrt(x+2))) ?
The first derivative of cos(x/(sqrt(x+2))) is -(sin(x/(sqrt(x+2)))(x+4))/(2(x+2)sqrt(x+2))