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Popular >

derivative of cos(ln(sqrt(x)))

Solution

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

Solution

- \frac{sin ( \frac{1}{2} ln ( x ) )}{2 x}

Solution steps

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

Apply the chain rule:

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

= - sin (ln (x)) \frac{d}{d x} (ln (x))

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

= - sin (ln (x)) \frac{1}{2 x}

Simplify

- sin (ln (x)) \frac{1}{2 x} : - \frac{sin ( \frac{1}{2} ln ( x ) )}{2 x}

= - \frac{sin ( \frac{1}{2} ln ( x ) )}{2 x}

Popular Examples

integral from 0 to 1 of (10sqrt(θ))/((1+θ^{3/2))^2}

\int_{0}^{1} \frac{10 θ}{( 1 + θ ^{\frac{3}{2}} ) ^{2}} d θ

derivative of x/((x^2-1^2))

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

derivative of f(x)=(e^x)/(x^6)derivative of

f (x) = \frac{e ^{x}}{x ^{6}}

integral of 4t^3sqrt(t^2+1)

\int 4 t^{3} t^{2} + 1 d t

y^'=(2y)/x-x^2y^2

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

Frequently Asked Questions (FAQ)

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