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Popular >

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

Solution

derivative of

r (x) = 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

derivative of 3arctan(x-sqrt(1+x^2))derivative of

3 arctan (x - 1 + x^{2})

derivative of o derivative of

o

integral of (3x^2-1/(x^2))

\int (3 x^{2} - \frac{1}{x ^{2}}) d x

y^'(1+e^x)=e^{x-y}

y^{^{'}} (1 + e^{x}) = e^{x - y}

(\partial)/(\partial x)(sin(x-y)+(x+y))

\frac{\partial}{\partial x} (sin (x - y) + (x + y))

Frequently Asked Questions (FAQ)

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