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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

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

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

Popular Examples

y^{''}-y^'-20y=0

y^{^{''}} - y^{^{'}} - 20 y = 0

(d^2)/(dx^2)(3x-4x^{9/10})

\frac{d ^{2}}{d x ^{2}} (3 x - 4 x^{\frac{9}{10}})

implicit (dy)/(dx),e^y=x+y implicit derivative

\frac{d y}{d x}, e^{y} = x + y

area 0.4x-1.295,-1.4206,-1.486 area

0.4 x - 1.295, - 1.4206, - 1.486

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n = 2 \sum \infty (- 0.75)^{n}

Frequently Asked Questions (FAQ)

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