What is (\partial)/(\partial x)((y)ln(5(x-1))) ?

The answer to (\partial)/(\partial x)((y)ln(5(x-1))) is y/(x-1)

Popular >

(\partial)/(\partial x)((y)ln(5(x-1)))

\frac{\partial}{\partial x} ((y) ln (5 (x - 1)))

\frac{y}{x - 1}

Solution steps

\frac{\partial}{\partial x} ((y) ln (5 (x - 1)))

Treat

y

as a constant

Take the constant out:

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

= y \frac{\partial}{\partial x} (ln (5 (x - 1)))

Apply the chain rule:

\frac{1}{5 ( x - 1 )} \frac{\partial}{\partial x} (5 (x - 1))

= \frac{1}{5 ( x - 1 )} \frac{\partial}{\partial x} (5 (x - 1))

\frac{\partial}{\partial x} (5 (x - 1)) = 5

= y \frac{1}{5 ( x - 1 )} \cdot 5

Simplify

y \frac{1}{5 ( x - 1 )} \cdot 5 : \frac{y}{x - 1}

= \frac{y}{x - 1}

e^{x} (16 x) - e^{x} (8 x^{2} + 2)

(y cos (x y) - 3 x^{2}) d x + (x cos (x y) + 3 y^{2}) d y

\frac{2}{9} x^{3} y^{2} - \frac{4}{3} x y^{3}

(1 - x) (1, 3, - 2)

\frac{81 ( 1 3 ^{15} - 1 )}{1 3 ^{15} \cdot 2}

What is (\partial)/(\partial x)((y)ln(5(x-1))) ?
The answer to (\partial)/(\partial x)((y)ln(5(x-1))) is y/(x-1)