What is (\partial)/(\partial x)(ln(x^{10}y)) ?

The answer to (\partial)/(\partial x)(ln(x^{10}y)) is (10)/x

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(\partial)/(\partial x)(ln(x^{10}y))

\frac{\partial}{\partial x} (ln (x^{10} y))

\frac{10}{x}

Solution steps

\frac{\partial}{\partial x} (ln (x^{10} y))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{10} y} \frac{\partial}{\partial x} (x^{10} y)

= \frac{1}{x ^{10} y} \frac{\partial}{\partial x} (x^{10} y)

\frac{\partial}{\partial x} (x^{10} y) = 10 y x^{9}

= \frac{1}{x ^{10} y} \cdot 10 y x^{9}

Simplify

\frac{1}{x ^{10} y} \cdot 10 y x^{9} : \frac{10}{x}

= \frac{10}{x}

f (x) = x^{2} - 2 x + 2

\frac{1 - x}{2}

(x 1 + y^{2}) d x - x^{2} d y = 0

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

2 x^{2}, 8 x^{2}, 5 - 3 x

What is (\partial)/(\partial x)(ln(x^{10}y)) ?
The answer to (\partial)/(\partial x)(ln(x^{10}y)) is (10)/x