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Popular >

derivative of ln(2+sin(x))

Solution

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

Solution

\frac{cos ( x )}{2 + sin ( x )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of (2x^2)/(3y^2)derivative of

\frac{2 x ^{2}}{3 y ^{2}}

y^{^{'}} + \frac{y}{x} = 4 x^{2}

(dy)/(dx)=(e^x)/(5+e^x)

\frac{d y}{d x} = \frac{e ^{x}}{5 + e ^{x}}

integral of ((ln(z))^3)/z

\int \frac{( ln ( z ) ) ^{3}}{z} d z

limit as x approaches 0 of 1/(4x)-1/((e^{4x)-1)}

x \to 0 lim (\frac{1}{4 x} - \frac{1}{( e ^{4 x} - 1 )})

Frequently Asked Questions (FAQ)

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