What is (\partial)/(\partial x)(x^2ln(y-1)) ?

The answer to (\partial)/(\partial x)(x^2ln(y-1)) is 2xln(y-1)

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(\partial)/(\partial x)(x^2ln(y-1))

\frac{\partial}{\partial x} (x^{2} ln (y - 1))

2 x ln (y - 1)

Solution steps

\frac{\partial}{\partial x} (x^{2} ln (y - 1))

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= ln (y - 1) \frac{\partial}{\partial x} (x^{2})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= ln (y - 1) \cdot 2 x^{2 - 1}

Simplify

= 2 x ln (y - 1)

\int_{1}^{2} x (x - 1)^{4} d x

\int ln (t) \cdot t^{2} d t

x \to + (- \infty) + lim (x^{5})

\frac{d y}{d x} = \frac{5 x}{2 y}

y = x^{- 3}, 1 \leq x \leq 6

What is (\partial)/(\partial x)(x^2ln(y-1)) ?
The answer to (\partial)/(\partial x)(x^2ln(y-1)) is 2xln(y-1)