What is the derivative of ln(x+sin(x+1)) ?

The derivative of ln(x+sin(x+1)) is (cos(x)+1)/(x+sin(x)+1)

What is the first derivative of ln(x+sin(x+1)) ?

The first derivative of ln(x+sin(x+1)) is (cos(x)+1)/(x+sin(x)+1)

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y = \frac{( x ^{2} + 1 ) ^{5}}{( 1 - x ^{2} ) ^{5}}

f (x) = \frac{ln ( x )}{2} + 2

sin (x)

\int 30 d x

2 x^{2} - 10 x

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