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

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

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

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

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derivative of

f (x) = ln (1 + sin^{2} (x))

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to - 0 lim (x^{2})

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

\frac{\partial}{\partial x} (x ln (2 y - x))

\frac{s - 3}{( s - 2 ) ^{2}}

x \to 0 lim (\frac{6 x - x ^{2}}{x})

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