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Popular >

derivative of ln(1+sin(2x))

Solution

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

Solution

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

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

Simplify

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

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

Popular Examples

integral of (x^3)/(x^3-7x+6)

\int \frac{x ^{3}}{x ^{3} - 7 x + 6} d x

(\partial)/(\partial y)(sin(3x+4y))

\frac{\partial}{\partial y} (sin (3 x + 4 y))

integral of (cos(t))/(1+sin(t))

\int \frac{cos ( t )}{1 + sin ( t )} d t

(\partial)/(\partial x)(x^2ln(x))

\frac{\partial}{\partial x} (x^{2} ln (x))

integral of (4x-2)/((x^2-x+1)^7)

\int \frac{4 x - 2}{( x ^{2} - x + 1 ) ^{7}} d x

Frequently Asked Questions (FAQ)

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