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

The derivative of sin(x^2+(1-x)/(1+x)) is cos(x^2)*2x-2/((1+x)^2)

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

The first derivative of sin(x^2+(1-x)/(1+x)) is cos(x^2)*2x-2/((1+x)^2)

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

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