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

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

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

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

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derivative of

1 + sin^{2} (x)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y^{^{'}} - \frac{2}{t} y = t^{2}

\frac{d}{d x} (- \frac{8 x}{( 4 x ^{2} + 1 ) ^{2}})

\frac{d}{d x} (arcsin (coth (x)))

ln (7 x)

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