What is the derivative of cos(x+ln(tan(x/2))) ?

The derivative of cos(x+ln(tan(x/2))) is cos(x)cot(x)

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

The first derivative of cos(x+ln(tan(x/2))) is cos(x)cot(x)

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\frac{d}{d x} (cos (x) + ln (tan (\frac{x}{2})))

cos (x) cot (x)

Solution steps

\frac{d}{d x} (cos (x) + ln (tan (\frac{x}{2})))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (ln (tan (\frac{x}{2}))) = csc (x)

= - sin (x) + csc (x)

Simplify

- sin (x) + csc (x) : cos (x) cot (x)

= cos (x) cot (x)

\frac{d}{d y} (ln (x^{2} + y^{2} + z^{2}))

f (x) = ln (2 x + 1)

\frac{x ^{2}}{x - 8}

\int x^{2} (x - 8)^{13} d x

\frac{\partial}{\partial x} (x y e^{x y})

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