What is the derivative of sin^2((x+2/(x+1))) ?

The derivative of sin^2((x+2/(x+1))) is -(sin(\frac{2(2+x))/(1+x))}{(1+x)^2}

What is the first derivative of sin^2((x+2/(x+1))) ?

The first derivative of sin^2((x+2/(x+1))) is -(sin(\frac{2(2+x))/(1+x))}{(1+x)^2}

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\frac{d}{d x} (sin^{2} (\frac{x + 2}{x + 1}))

- \frac{sin ( \frac{2 ( 2 + x )}{1 + x} )}{( 1 + x ) ^{2}}

Solution steps

\frac{d}{d x} (sin^{2} (\frac{x + 2}{x + 1}))

Apply the chain rule:

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

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

\frac{d}{d x} (sin (\frac{x + 2}{x + 1})) = - \frac{cos ( \frac{x + 2}{x + 1} )}{( x + 1 ) ^{2}}

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

Simplify

2 sin (\frac{x + 2}{x + 1}) (- \frac{cos ( \frac{x + 2}{x + 1} )}{( x + 1 ) ^{2}}) : - \frac{sin ( \frac{2 ( 2 + x )}{1 + x} )}{( 1 + x ) ^{2}}

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

y^{^{'}} = ln (x) y + x^{x}

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

\int_{0}^{2} x^{2} (x^{3} + 1)^{\frac{3}{2}} d x

3 x^{2}, x^{2} + 4, - 2, 2

ln (\frac{x}{x ^{2} + 6})

What is the derivative of sin^2((x+2/(x+1))) ?
The derivative of sin^2((x+2/(x+1))) is -(sin(\frac{2(2+x))/(1+x))}{(1+x)^2}
What is the first derivative of sin^2((x+2/(x+1))) ?
The first derivative of sin^2((x+2/(x+1))) is -(sin(\frac{2(2+x))/(1+x))}{(1+x)^2}