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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{3}{4} t + 6 d t

x \to 3 - lim (9 - x^{2})

f (x) = \frac{x + 2}{x ^{2} - 9}, at x = 1

\int 3 x - 12 d x

\frac{d}{d x} (\frac{3}{2 x} + \frac{4 x}{5})

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