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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int (x + 4)^{2} d x

x \to 7 lim (\frac{x - 7}{3 x ^{2} - 21 x})

\frac{\partial}{\partial x} (ln (x) + z ln (y))

y^{^{''}} + 7 y^{^{'}} + 10 y = 3 e^{4 t}

\frac{d}{d x} (A x e^{x^{2}})

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