What is the derivative of sin(x/(sqrt(x+1))) ?

The derivative of sin(x/(sqrt(x+1))) is (cos(x/(sqrt(x+1)))(x+2))/(2(x+1)sqrt(x+1))

What is the first derivative of sin(x/(sqrt(x+1))) ?

The first derivative of sin(x/(sqrt(x+1))) is (cos(x/(sqrt(x+1)))(x+2))/(2(x+1)sqrt(x+1))

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\frac{d}{d x} (sin (\frac{x}{x + 1}))

\frac{cos ( \frac{x}{x + 1} ) ( x + 2 )}{2 ( x + 1 ) x + 1}

Solution steps

\frac{d}{d x} (sin (\frac{x}{x + 1}))

Apply the chain rule:

cos (\frac{x}{x + 1}) \frac{d}{d x} (\frac{x}{x + 1})

= cos (\frac{x}{x + 1}) \frac{d}{d x} (\frac{x}{x + 1})

\frac{d}{d x} (\frac{x}{x + 1}) = \frac{x + 2}{2 ( x + 1 ) x + 1}

= cos (\frac{x}{x + 1}) \frac{x + 2}{2 ( x + 1 ) x + 1}

Multiply fractions:

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

= \frac{cos ( \frac{x}{x + 1} ) ( x + 2 )}{2 ( x + 1 ) x + 1}

x \to 7 lim ((x - 7)^{2} + x^{2})

x \to 0 + lim (ln (\frac{1}{x ^{4}}))

u (x) = x

f (x) = 3 x^{3} + 15 x^{2} + 29 x + 3

\int \frac{25 x ^{2} - 64}{x ^{3}} d x

What is the derivative of sin(x/(sqrt(x+1))) ?
The derivative of sin(x/(sqrt(x+1))) is (cos(x/(sqrt(x+1)))(x+2))/(2(x+1)sqrt(x+1))
What is the first derivative of sin(x/(sqrt(x+1))) ?
The first derivative of sin(x/(sqrt(x+1))) is (cos(x/(sqrt(x+1)))(x+2))/(2(x+1)sqrt(x+1))