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

The derivative of (sin^2(x+1)/(cos^2(x)+1)) is (3sin(2x))/((cos^2(x)+1)^2)

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

The first derivative of (sin^2(x+1)/(cos^2(x)+1)) is (3sin(2x))/((cos^2(x)+1)^2)

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

\frac{3 sin ( 2 x )}{( cos ^{2} ( x ) + 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{sin ( 2 x ) ( cos ^{2} ( x ) + 1 ) - ( - sin ( 2 x ) ) ( sin ^{2} ( x ) + 1 )}{( cos ^{2} ( x ) + 1 ) ^{2}} : \frac{3 sin ( 2 x )}{( cos ^{2} ( x ) + 1 ) ^{2}}

= \frac{3 sin ( 2 x )}{( cos ^{2} ( x ) + 1 ) ^{2}}

\frac{x}{8}

{\frac{( s - 1 )}{s + 1}}

\frac{\partial}{\partial y} (e^{x y} + x^{2} z)

\frac{x ^{4}}{1 - x ^{3}}

x^{2}, (- 2, 1)

What is the derivative of (sin^2(x+1)/(cos^2(x)+1)) ?
The derivative of (sin^2(x+1)/(cos^2(x)+1)) is (3sin(2x))/((cos^2(x)+1)^2)
What is the first derivative of (sin^2(x+1)/(cos^2(x)+1)) ?
The first derivative of (sin^2(x+1)/(cos^2(x)+1)) is (3sin(2x))/((cos^2(x)+1)^2)