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Popular >

derivative of tan(sqrt(1-x))

Solution

\frac{d}{d x} (tan (1 - x))

Solution

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

Solution steps

\frac{d}{d x} (tan (1 - x))

Apply the chain rule:

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

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

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

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

Simplify

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

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

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x \to 0 + lim (x \cdot (e^{\frac{1}{x}} - 1))

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Frequently Asked Questions (FAQ)

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