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Popular Calculus >

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

Popular Examples

(\partial)/(\partial x)(e^{x/y}(1-x/y))

\frac{\partial}{\partial x} (e^{\frac{x}{y}} (1 - \frac{x}{y}))

y^'=(x^2+y^2)/(2xy)

y^{^{'}} = \frac{x ^{2} + y ^{2}}{2 x y}

(\partial)/(\partial u(v))((e^v)/(u(v)+v^5))

\frac{\partial}{\partial u ( v )} (\frac{e ^{v}}{u ( v ) + v ^{5}})

derivative of x/(sqrt(x^2+4))

\frac{d}{d x} (\frac{x}{x ^{2} + 4})

limit as x approaches 25 of log_{5}(x)

x \to 25 lim (lo g_{5} (x))

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))