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derivative of sin(x^2)+((1-x))/(1+x)

Solution

derivative of

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

Solution

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}}

Popular Examples

(\partial)/(\partial x)(2/(x+2y))

\frac{\partial}{\partial x} (\frac{2}{x + 2 y})

derivative of ((x^2-1)/(x^2+x+1))

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

derivative of-1-4sin(x)

\frac{d}{d x} (- 1 - 4 sin (x))

sum from k=0 to infinity of 5x^k

k = 0 \sum \infty 5 x^{k}

inverse oflaplace (s+5)/(s^2-4s+4)inverse laplace

\frac{s + 5}{s ^{2} - 4 s + 4}

Frequently Asked Questions (FAQ)

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)