What is the derivative of sin(sqrt(x-1)) ?

The derivative of sin(sqrt(x-1)) is (cos(sqrt(x-1)))/(2sqrt(x-1))

What is the first derivative of sin(sqrt(x-1)) ?

The first derivative of sin(sqrt(x-1)) is (cos(sqrt(x-1)))/(2sqrt(x-1))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 2 lim (2 x)

y^{^{''}} - 4 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 5

y^{^{''}} - y = e^{t}

\int \frac{24 q}{4 q ^{2} + 7} d q

\frac{\partial}{\partial x} (2 x^{2} y + 3 x y^{3})

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