What is (\partial)/(\partial x)(sin(ln(x))) ?

The answer to (\partial)/(\partial x)(sin(ln(x))) is (cos(ln(x)))/x

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(\partial)/(\partial x)(sin(ln(x)))

\frac{\partial}{\partial x} (sin (ln (x)))

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

Solution steps

\frac{\partial}{\partial x} (sin (ln (x)))

Apply the chain rule:

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

= cos (ln (x)) \frac{\partial}{\partial x} (ln (x))

\frac{\partial}{\partial x} (ln (x)) = \frac{1}{x}

= cos (ln (x)) \frac{1}{x}

Simplify

cos (ln (x)) \frac{1}{x} : \frac{cos ( ln ( x ) )}{x}

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

\frac{\partial}{\partial y} (x^{- 7} y^{2} + x y^{2} + 3 x y)

\frac{d y}{d x} = - 10 y, y (0) = 5

\int_{0}^{\frac{1}{2}} 8 x (\frac{1}{2} - x) d x

\frac{\partial}{\partial x} (x \cdot sin (x) - 1)

n = 1 \sum \infty n e^{- \frac{n}{2}}

What is (\partial)/(\partial x)(sin(ln(x))) ?
The answer to (\partial)/(\partial x)(sin(ln(x))) is (cos(ln(x)))/x