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Popular >

derivative of tan(cos(x/2))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

sec^{2} (cos (\frac{x}{2})) \frac{d}{d x} (cos (\frac{x}{2}))

= sec^{2} (cos (\frac{x}{2})) \frac{d}{d x} (cos (\frac{x}{2}))

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

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

Simplify

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

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\int e^{x^{3} + 5} \cdot x^{2} d x

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\int \frac{8 - e ^{x}}{e ^{5 x}} d x

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\int \frac{x}{x ^{4}} d x

Frequently Asked Questions (FAQ)

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