What is the derivative of 4/(5+cos(x)) ?

The derivative of 4/(5+cos(x)) is (4sin(x))/((5+cos(x))^2)

What is the first derivative of 4/(5+cos(x)) ?

The first derivative of 4/(5+cos(x)) is (4sin(x))/((5+cos(x))^2)

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\frac{d}{d x} (\frac{4}{5 + cos ( x )})

\frac{4 sin ( x )}{( 5 + cos ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4}{5 + cos ( x )})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (\frac{1}{5 + cos ( x )})

Apply exponent rule:

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

= 4 \frac{d}{d x} ((5 + cos (x))^{- 1})

Apply the chain rule:

- \frac{1}{( 5 + cos ( x ) ) ^{2}} \frac{d}{d x} (5 + cos (x))

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

\frac{d}{d x} (5 + cos (x)) = - sin (x)

= 4 (- \frac{1}{( 5 + cos ( x ) ) ^{2}} (- sin (x)))

Simplify

4 (- \frac{1}{( 5 + cos ( x ) ) ^{2}} (- sin (x))) : \frac{4 sin ( x )}{( 5 + cos ( x ) ) ^{2}}

= \frac{4 sin ( x )}{( 5 + cos ( x ) ) ^{2}}

f (x) = 8 (x - \frac{1}{x})^{2}, at x = 2

\frac{d}{d x} (1 0^{- 3 x^{2}})

\int x^{2} + 49 d x

y = 2 x, y = \frac{2 x}{3}

\frac{d}{d x} (2 x + y)^{3} = x

What is the derivative of 4/(5+cos(x)) ?
The derivative of 4/(5+cos(x)) is (4sin(x))/((5+cos(x))^2)
What is the first derivative of 4/(5+cos(x)) ?
The first derivative of 4/(5+cos(x)) is (4sin(x))/((5+cos(x))^2)