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

The derivative of (sin(1+x^2))/((1-x^2)) is (2xcos(1+x^2)(1-x^2)+2xsin(1+x^2))/((1-x^2)^2)

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

The first derivative of (sin(1+x^2))/((1-x^2)) is (2xcos(1+x^2)(1-x^2)+2xsin(1+x^2))/((1-x^2)^2)

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

(2 x - 4)^{3}

sin^{2} (x) - x

y = (3 x^{3} - 5 x^{2} + 3) 7

y = sin (x^{2} + 1)

\frac{d}{d t} ((c_{1} + c, t) \cdot e^{t})

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