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Popular >

derivative of sin(sqrt(x^2-1))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Graph

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Frequently Asked Questions (FAQ)

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