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Popular >

derivative of sin((sqrt(5)/2 ln(x)))

Solution

\frac{d}{d x} (sin (\frac{5}{2} ln (x)))

Solution

\frac{5 cos ( \frac{5}{2} ln ( x ) )}{2 x}

Solution steps

\frac{d}{d x} (sin (\frac{5}{2} ln (x)))

Apply the chain rule:

cos (\frac{5}{2} ln (x)) \frac{d}{d x} (\frac{5}{2} ln (x))

= cos (\frac{5}{2} ln (x)) \frac{d}{d x} (\frac{5}{2} ln (x))

\frac{d}{d x} (\frac{5}{2} ln (x)) = \frac{5}{2 x}

= cos (\frac{5}{2} ln (x)) \frac{5}{2 x}

Multiply fractions:

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

= \frac{5 cos ( \frac{5}{2} ln ( x ) )}{2 x}

Popular Examples

integral of (sin(kt))/(a+cos(kt))

\int \frac{sin ( k t )}{a + cos ( k t )} d t

limit as x approaches 3 of 3x^2+4x-1

x \to 3 lim (3 x^{2} + 4 x - 1)

limit as x approaches 0 of (x-2)/(x-2)

x \to 0 lim (\frac{x - 2}{x - 2})

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

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

(\partial)/(\partial x)(x^2+y^2+z^2-9)

\frac{\partial}{\partial x} (x^{2} + y^{2} + z^{2} - 9)

Frequently Asked Questions (FAQ)

What is the derivative of sin((sqrt(5)/2 ln(x))) ?
The derivative of sin((sqrt(5)/2 ln(x))) is (sqrt(5)cos((sqrt(5))/2 ln(x)))/(2x)
What is the first derivative of sin((sqrt(5)/2 ln(x))) ?
The first derivative of sin((sqrt(5)/2 ln(x))) is (sqrt(5)cos((sqrt(5))/2 ln(x)))/(2x)